#### Prof. Dr. Götz S. Uhrig

Theoretical Physics

TU Dortmund University

##### Contact

- goetz.uhrig@tu-dortmund.de
- +49 231 755 3547
- personal website

##### Hub

**Dynamical properties of a driven dissipative dimerized S= 12 chain**

Yarmohammadi, M. and Meyer, C. and Fauseweh, B. and Normand, B. and Uhrig, G.S.*Physical Review B*103 (2021)We consider the dynamical properties of a gapped quantum spin system coupled to the electric field of a laser, which drives the resonant excitation of specific phonon modes that modulate the magnetic interactions. We deduce the quantum master equations governing the time-evolution of both the lattice and spin sectors, by developing a Lindblad formalism with bath operators providing an explicit description of their respective phonon-mediated damping terms. We investigate the nonequilibrium steady states (NESS) of the spin system established by a continuous driving, delineating parameter regimes in driving frequency, damping, and spin-phonon coupling for the establishment of physically meaningful NESS and their related nontrivial properties. Focusing on the regime of generic weak spin-phonon coupling, we characterize the NESS by their frequency and wave-vector content, explore their transient and relaxation behavior, and discuss the energy flow, the system temperature, and the critical role of the type of bath adopted. Our study lays a foundation for the quantitative modeling of experiments currently being designed to control coherent many-body spin states in quantum magnetic materials. © 2021 American Physical Society.view abstract 10.1103/PhysRevB.103.045132 **Nuclear magnetic resonance spectroscopy of nonequilibrium steady states in quantum dots**

Schering, P. and Uhrig, G.S.*EPL*133 (2021)The optically induced polarization of localized electron spins in an ensemble of quantum dots (QDs) dephases due to the interaction with the surrounding nuclear spins. Despite this dephasing, the spins in the QDs can be controlled to respond coherently by applying periodic laser pulses, leading to a revival of the spin polarization before each pulse. This effect, known as spin mode locking, strongly depends on an emerging selection of certain polarizations of the nuclear spin bath which is driven to a steady state far from equilibrium. We investigate the influence of the nuclear composition in In x Ga1-x As QDs on this nonequilibrium behavior and demonstrate that nuclear magnetic resonances (NMR) appear as very sharp minima in the magnetic field dependence of the revival amplitude. This suggests a novel kind of NMR spectroscopy. © Copyright2021 EPLA.view abstract 10.1209/0295-5075/133/57003 **Resonant spin amplification in Faraday geometry**

Schering, P. and Evers, E. and Nedelea, V. and Smirnov, D.S. and Zhukov, E.A. and Yakovlev, D.R. and Bayer, M. and Uhrig, G.S. and Greilich, A.*Physical Review B*103 (2021)We demonstrate the realization of the resonant spin amplification (RSA) effect in Faraday geometry where a magnetic field is applied parallel to the optically induced spin polarization so that no RSA is expected. However, model considerations predict that it can be realized for a central spin interacting with a fluctuating spin environment. As a demonstrator, we choose an ensemble of singly-charged (In,Ga)As/GaAs quantum dots, where the resident electron spins interact with the surrounding nuclear spins. The observation of RSA in Faraday geometry requires intense pump pulses with a high repetition rate and can be enhanced by means of the spin-inertia effect. Potentially, it provides the most direct and reliable tool to measure the longitudinal g factor of the charge carriers. © 2021 American Physical Society.view abstract 10.1103/PhysRevB.103.L201301 **The 2021 Magnonics Roadmap**

Barman, A. and Gubbiotti, G. and Ladak, S. and Adeyeye, A.O. and Krawczyk, M. and Grafe, J. and Adelmann, C. and Cotofana, S. and Naeemi, A. and Vasyuchka, V.I. and Hillebrands, B. and Nikitov, S.A. and Yu, H. and Grundler, D. and Sadovnikov, A.V. and Grachev, A.A. and Sheshukova, S.E. and Duquesne, J.-Y. and Marangolo, M. and Csaba, G. and Porod, W. and Demidov, V.E. and Urazhdin, S. and Demokritov, S.O. and Albisetti, E. and Petti, D. and Bertacco, R. and Schultheiss, H. and Kruglyak, V.V. and Poimanov, V.D. and Sahoo, S. and Sinha, J. and Yang, H. and Münzenberg, M. and Moriyama, T. and Mizukami, S. and Landeros, P. and Gallardo, R.A. and Carlotti, G. and Kim, J.-V. and Stamps, R.L. and Camley, R.E. and Rana, B. and Otani, Y. and Yu, W. and Yu, T. and Bauer, G.E.W. and Back, C. and Uhrig, G.S. and Dobrovolskiy, O.V. and Budinska, B. and Qin, H. and Van Dijken, S. and Chumak, A.V. and Khitun, A. and Nikonov, D.E. and Young, I.A. and Zingsem, B.W. and Winklhofer, M.*Journal of Physics Condensed Matter*33 (2021)Magnonics is a budding research field in nanomagnetism and nanoscience that addresses the use of spin waves (magnons) to transmit, store, and process information. The rapid advancements of this field during last one decade in terms of upsurge in research papers, review articles, citations, proposals of devices as well as introduction of new sub-topics prompted us to present the first roadmap on magnonics. This is a collection of 22 sections written by leading experts in this field who review and discuss the current status besides presenting their vision of future perspectives. Today, the principal challenges in applied magnonics are the excitation of sub-100 nm wavelength magnons, their manipulation on the nanoscale and the creation of sub-micrometre devices using low-Gilbert damping magnetic materials and its interconnections to standard electronics. To this end, magnonics offers lower energy consumption, easier integrability and compatibility with CMOS structure, reprogrammability, shorter wavelength, smaller device features, anisotropic properties, negative group velocity, non-reciprocity and efficient tunability by various external stimuli to name a few. Hence, despite being a young research field, magnonics has come a long way since its early inception. This roadmap asserts a milestone for future emerging research directions in magnonics, and hopefully, it will inspire a series of exciting new articles on the same topic in the coming years. © 2021 The Author(s). Published by IOP Publishing Ltd.view abstract 10.1088/1361-648X/abec1a **Classification and characterization of nonequilibrium Higgs modes in unconventional superconductors**

Schwarz, L. and Fauseweh, B. and Tsuji, N. and Cheng, N. and Bittner, N. and Krull, H. and Berciu, M. and Uhrig, G.S. and Schnyder, A.P. and Kaiser, S. and Manske, D.*Nature Communications*11 (2020)Recent findings of new Higgs modes in unconventional superconductors require a classification and characterization of the modes allowed by nontrivial gap symmetry. Here we develop a theory for a tailored nonequilibrium quantum quench to excite all possible oscillation symmetries of a superconducting condensate. We show that both a finite momentum transfer and quench symmetry allow for an identification of the resulting Higgs oscillations. These serve as a fingerprint for the ground state gap symmetry. We provide a classification scheme of these oscillations and the quench symmetry based on group theory for the underlying lattice point group. For characterization, analytic calculations as well as full scale numeric simulations of the transient optical response resulting from an excitation by a realistic laser pulse are performed. Our classification of Higgs oscillations allows us to distinguish between different symmetries of the superconducting condensate. © 2020, The Author(s).view abstract 10.1038/s41467-019-13763-5 **Exchange-mediated magnetic blue-shift of the band-gap energy in the antiferromagnetic semiconductor MnTe**

Bossini, D. and Terschanski, M. and Mertens, F. and Springholz, G. and Bonanni, A. and Uhrig, G.S. and Cinchetti, M.*New Journal of Physics*22 (2020)In magnetic semiconductors the optical spectrum and, in particular, the absorption edge representing the band-gap are strongly affected by the onset of the magnetic order. This contribution to the band-gap energy has hitherto been described theoretically in terms of a Heisenberg Hamiltonian, in which a delocalized conduction carrier is coupled to the localized magnetic moments by the exchange interaction. Such models, however, do not take into account the strong correlations displayed in a wide variety of magnetic semiconductors, which are responsible for the formation of the local moments. In particular, the itinerant carrier itself contributes to the spin moment. Here, we overcome this simplification in a combined experimental and theoretical study of the antiferromagnetic semiconductor α-MnTe. First, we present a spectroscopic optical investigation as a function of temperature, from which we extract the magnetic contribution to the blue-shift of the band-gap. Second, we formulate a minimal model based on a Hubbard-Kondo Hamiltonian. In this model, the itinerant charge is one of the electrons forming the localized magnetic moment, which properly captures correlation effects in the material. Our theory reproduces the experimental findings with excellent quantitative agreement, demonstrating that the magnetic contribution to the band-gap energy of α-MnTe is mediated solely by the exchange interaction. These results describe an intrinsic property of the material, independent of the thickness, substrate and capping layer of the specimen. One of the key findings of the model is that the basic effect, namely a blue-shift of the band-gap due to the establishment of the magnetic order, is a general phenomenon in charge-transfer insulators. The identification of the relevant magnetic interaction discloses the possibility to exploit the effect here discussed to induce a novel regime of coherent spin dynamics, in which spin oscillations on a characteristic time-scale of 100 fs are triggered and are intrinsically coupled to charges. © 2020 The Author(s). Published by IOP Publishing Ltd on behalf of the Institute of Physics and Deutsche Physikalische Gesellschaft.view abstract 10.1088/1367-2630/aba0e7 **Interplay of spin mode locking and nuclei-induced frequency focusing in quantum dots**

Schering, P. and Scherer, P.W. and Uhrig, G.S.*Physical Review B*102 (2020)We study the influence of nuclei-induced frequency focusing on the mode locking of spin coherence in quantum dots subjected to a periodic train of optical pulses. In particular, we address the question whether or not nuclei-induced frequency focusing always enhances the effect of spin mode locking. We combine two advanced semiclassical approaches and extend the resulting model by including the full dynamics of the optically excited trion state. In order to reduce the discrepancy to a full quantum model, we establish a nondeterministic pulse description by interpreting each pump pulse as a measurement. Both extensions lead to significant qualitative changes of the physics. Their combination improves the description of the corresponding experiments. Importantly, we observe the emergence of dynamic nuclear polarization, i.e., the formation of a nonzero average polarization of the nuclear spin bath, leading to a certain increase of the coherence time. © 2020 American Physical Society.view abstract 10.1103/PhysRevB.102.115301 **Probing thermalization in quenched integrable and nonintegrable Fermi-Hubbard models**

Bleicker, P. and Stolze, J. and Uhrig, G.S.*Physical Review A*102 (2020)Using numerically exact methods we examine the Fermi-Hubbard model on arbitrary cluster topology. We focus on the question of which systems eventually equilibrate or even thermalize after an interaction quench when initially prepared in a state highly entangled between system and bath. We find that constants of motion in integrable clusters prevent equilibration to the thermal state. We discuss the size of fluctuations during equilibration and thermalization and the influence of integrability. The influence of real-space topology and in particular of infinite-range graphs on equilibration and thermalization is studied. © 2020 American Physical Society.view abstract 10.1103/PhysRevA.102.013321 **Quantum coherence from commensurate driving with laser pulses and decay**

Uhrig, G.S.*SciPost Physics*8 (2020)Non-equilibrium physics is a particularly fascinating field of current research. Generically, driven systems are gradually heated up so that quantum effects die out. In contrast, we show that a driven central spin model including controlled dissipation in a highly excited state allows us to distill quantum coherent states, indicated by a substantial reduction of entropy; the key resource is the commensurability between the periodicity of the pump pulses and the internal processes. The model is experimentally accessible in purified quantum dots or molecules with unpaired electrons. The potential of preparing and manipulating coherent states by designed driving potentials is pointed out. Copyright G. S. Uhrig. This work is licensed under the Creative Commons Attribution 4.0 International License. Published by the SciPost Foundation.view abstract 10.21468/SciPostPhys.8.3.040 **Topological magnetic excitations**

Malki, M. and Uhrig, G.S.*EPL*132 (2020)Topological properties play an increasingly important role in future research and technology. This also applies to the field of topological magnetic excitations which has recently become a very active and broad field. In this Perspective article, we give an insight into the current theoretical and experimental investigations and try an outlook on future lines of research. Copyright © 2020 EPLAview abstract 10.1209/0295-5075/132/20003 **Topological superconductivity induced by a triple- q magnetic structure**

Bedow, J. and Mascot, E. and Posske, T. and Uhrig, G.S. and Wiesendanger, R. and Rachel, S. and Morr, D.K.*Physical Review B*102 (2020)We demonstrate that the recently discovered triple-q (3q) magnetic structure, when embedded in a magnet-superconductor hybrid (MSH) system, gives rise to the emergence of topological superconductivity. We investigate the structure of chiral Majorana edge modes at domain walls, and show that they can be distinguished from trivial in-gap modes through the spatial distribution of the induced supercurrents. Finally, we show that topological superconductivity in 3q MSH systems is a robust phenomenon that does not depend on the relative alignment of the magnetic and superconducting layers, or on the presence of electronic degrees of freedom in the magnetic layer. © 2020 American Physical Society.view abstract 10.1103/PhysRevB.102.180504 **Tunable signal velocity in the integer quantum hall effect of tailored graphene**

Malki, M. and Uhrig, G.S.*Journal of the Physical Society of Japan*89 (2020)Topological properties in condensed matter physics are often claimed to be a fruitful resource for technical applications, but so far they only play a minor role in applications. Here we propose to put topological edge states to use in tailored graphene for Fermi velocity engineering. By tuning external control parameters such as gate voltages, the dispersions of the edge states regime are modified in a controllable way. This enables the realizations of devices such as tunable delay lines and interferometers with switchable delays. © 2020 The Physical Society of Japan.view abstract 10.7566/JPSJ.89.054705 **Delocalization of edge states in topological phases**

Malki, M. and Uhrig, G.S.*EPL*127 (2019)The presence of a topologically non-trivial discrete invariant implies the existence of gapless modes in finite samples, but it does not necessarily imply their localization. The disappearance of the indirect energy gap in the bulk generically leads to the absence of localized edge states. We illustrate this behavior in two fundamental lattice models on the single-particle level. By tuning a hopping parameter the indirect gap is closed while maintaining the topological properties. The inverse participation ratio is used to measure the degree of localization. © 2019 EPLA.view abstract 10.1209/0295-5075/127/27001 **Positivity of the Spectral Densities of Retarded Floquet Green Functions**

Uhrig, G.S. and Kalthoff, M.H. and Freericks, J.K.*Physical Review Letters*122 (2019)Periodically driven nonequilibrium many-body systems are interesting because they have quasi-energy spectra, which can be tailored by controlling the external driving fields. We derive the general spectral representation of retarded Green functions in the Floquet regime, thereby generalizing the well-known Lehmann representation from equilibrium many-body physics. The derived spectral Floquet representation allows us to prove the non-negativity of spectral densities and to determine exact spectral sum rules, which can be employed to benchmark the accuracy of approximations to the exact Floquet many-body Green functions. © 2019 American Physical Society.view abstract 10.1103/PhysRevLett.122.130604 **Time-crystalline behavior in an engineered spin chain**

Schäfer, R. and Uhrig, G.S. and Stolze, J.*Physical Review B*100 (2019)Time crystals break the discrete time translational invariance of an external periodic drive by oscillating at an integer multiple of the driving period. In addition to this fundamental property, other aspects are often considered to be essential characteristics of a time crystal, such as the presence of disorder or interactions, robustness against small variations of system parameters, and the free choice of the initial quantum state. We study a finite-length polarized XX spin chain engineered to display a spectrum of equidistant energy levels without drive and show that it keeps a spectrum of equidistant Floquet quasienergies when subjected to a large variety of periodic driving schemes. Arbitrary multiples of the driving period can then be reached by adjusting parameters of the drive, for arbitrary initial states. This behavior is understood by mapping the XX spin chain with N+1 sites to a single large spin with S=N/2 invoking the closure of the group SU(2). Our simple model is neither intrinsically disordered nor is it an interacting many-body system (after suitable mapping), and it does not have a thermodynamic limit in the conventional sense. It does, however, show controllable discrete time translational symmetry breaking for arbitrary initial states and a degree of robustness against perturbations, thereby carrying some characteristic traits of a discrete time crystal. © 2019 American Physical Society.view abstract 10.1103/PhysRevB.100.184301 **Topological magnon bands for magnonics**

Malki, M. and Uhrig, G.S.*Physical Review B*99 (2019)Topological excitations in magnetically ordered systems have attracted much attention lately. We report on topological magnon bands in ferromagnetic Shastry-Sutherland lattices whose edge modes can be put to use in magnonic devices. The synergy of Dzyaloshinskii-Moriya interactions and geometrical frustration are responsible for the topologically nontrivial character. Using exact spin-wave theory, we determine the finite Chern numbers of the magnon bands which give rise to chiral edge states. The quadratic band crossing point vanishes due the present anisotropies, and the system enters a topological phase. We calculate the thermal Hall conductivity as an experimental signature of the topological phase. Different promising compounds are discussed as possible physical realizations of ferromagnetic Shastry-Sutherland lattices hosting the required antisymmetric Dzyaloshinskii-Moriya interactions. Routes to applications in magnonics are pointed out. © 2019 American Physical Society.view abstract 10.1103/PhysRevB.99.174412 **Emergence of Floquet behavior for lattice fermions driven by light pulses**

Kalthoff, M.H. and Uhrig, G.S. and Freericks, J.K.*Physical Review B*98 (2018)As many-body Floquet theory becomes more popular, it is important to find ways to connect theory with experiment. Theoretical calculations can have a periodic driving field that is always on, but experiment cannot. Hence, we need to know how long a driving field is needed before the system starts to look like the periodically driven Floquet system. We answer this question here for noninteracting band electrons in the infinite-dimensional limit by studying the properties of the system under pulsed driving fields and illustrating how they approach the Floquet limit. Our focus is on determining the minimal pulse lengths needed to recover the qualitative and semiquantitative Floquet theory results. © 2018 American Physical Society.view abstract 10.1103/PhysRevB.98.035138 **Magnetic field dependence of the electron spin revival amplitude in periodically pulsed quantum dots**

Kleinjohann, I. and Evers, E. and Schering, P. and Greilich, A. and Uhrig, G.S. and Bayer, M. and Anders, F.B.*Physical Review B*98 (2018)Periodic laser pulsing of singly charged semiconductor quantum dots in an external magnetic field leads to a synchronization of the spin dynamics with the optical excitation. The pumped electron spins partially rephase prior to each laser pulse, causing a revival of electron spin polarization with its maximum at the incidence time of a laser pulse. The amplitude of this revival is amplified by the frequency focusing of the surrounding nuclear spins. Two complementary theoretical approaches for simulating up to 20 million laser pulses are developed and employed that are able to bridge between 11 orders of magnitude in time: a fully quantum mechanical description limited to small nuclear bath sizes and a technique based on the classical equations of motion applicable for a large number of nuclear spins. We present experimental data of the nonmonotonic revival amplitude as function of the magnetic field applied perpendicular to the optical axis. The dependence of the revival amplitude on the external field with a profound minimum at 4T is reproduced by both of our theoretical approaches and is ascribed to the nuclear Zeeman effect. Since the nuclear Larmor precession determines the electronic resonance condition, it also defines the number of electron spin revolutions between pump pulses, the orientation of the electron spin at the incidence time of a pump pulse, and the resulting revival amplitude. The magnetic field of 4T, for example, corresponds to half a revolution of nuclear spins between two laser pulses. © 2018 American Physical Society.view abstract 10.1103/PhysRevB.98.155318 **Nuclear frequency focusing in periodically pulsed semiconductor quantum dots described by infinite classical central spin models**

Schering, P. and Hüdepohl, J. and Uhrig, G.S. and Fauseweh, B.*Physical Review B*98 (2018)The coherence of an electronic spin in a semiconductor quantum dot decays due to its interaction with the bath of nuclear spins in the surrounding isotopes. This effect can be reduced by subjecting the system to an external magnetic field and by applying optical pulses. By repeated pulses in long trains the spin precession can be synchronized to the pulse period TR. This drives the nuclear spin bath into states far from equilibrium leading to nuclear frequency focusing. In this paper, we use an efficient classical approach introduced in Fauseweh et al. [Fauseweh, Schering, Hüdepohl, and Uhrig, Phys. Rev. B 96, 054415 (2017)2469-995010.1103/PhysRevB.96.054415] to describe and to analyze this nuclear focusing. Its dependence on the effective bath size and on the external magnetic field is elucidated in a comprehensive study. We find that the characteristics of the pulse as well as the nuclear Zeeman effect influence the behavior decisively. © 2018 American Physical Society.view abstract 10.1103/PhysRevB.98.024305 **Quantum mechanical treatment of large spin baths**

Röhrig, R. and Schering, P. and Gravert, L.B. and Fauseweh, B. and Uhrig, G.S.*Physical Review B*97 (2018)The electronic spin in quantum dots can be described by central spin models (CSMs) with a very large number Neff≈104 to 106 of bath spins posing a tremendous challenge to theoretical simulations. Here, a fully quantum mechanical theory is developed for the limit Neff→ by means of iterated equations of motion (iEoM). We find that the CSM can be mapped to a four-dimensional impurity coupled to a noninteracting bosonic bath in this limit. Remarkably, even for infinite bath the CSM does not become completely classical. The data obtained by the proposed iEoM approach are tested successfully against data from other, established approaches. Thus the iEoM mapping extends the set of theoretical tools that can be used to understand the spin dynamics in large CSMs. © 2018 American Physical Society.view abstract 10.1103/PhysRevB.97.165431 **Strong quenches in the one-dimensional Fermi-Hubbard model**

Bleicker, P. and Uhrig, G.S.*Physical Review A*98 (2018)The one-dimensional Fermi-Hubbard model is used as test bed for strong global parameter quenches. With the aid of iterated equations of motion in combination with a suitable scalar product for operators, we describe the dynamics and the long-term behavior in particular of the system after interaction quenches. This becomes possible because the employed approximation allows for oscillatory dynamics avoiding spurious divergences. The infinite-time behavior is captured by an analytical approach based on stationary phases; no numerical averages over long times need to be computed. We study the most relevant frequencies in the dynamics after the quench and find that the local interaction U as well as the bandwidth W dominate. In contrast to former studies, a crossover instead of a sharp dynamical transition depending on the strength of the quench is identified. For weak quenches, the bandwidth is more important while for strong quenches the local interaction U dominates. © 2018 American Physical Society.view abstract 10.1103/PhysRevA.98.033602 **Comparison of the iterated equation of motion approach and the density matrix formalism for the quantum Rabi model**

Kalthoff, M. and Keim, F. and Krull, H. and Uhrig, G.S.*European Physical Journal B*90 (2017)The density matrix formalism and the equation of motion approach are two semi-analytical methods that can be used to compute the non-equilibrium dynamics of correlated systems. While for a bilinear Hamiltonian both formalisms yield the exact result, for any non-bilinear Hamiltonian a truncation is necessary. Due to the fact that the commonly used truncation schemes differ for these two methods, the accuracy of the obtained results depends significantly on the chosen approach. In this paper, both formalisms are applied to the quantum Rabi model. This allows us to compare the approximate results and the exact dynamics of the system and enables us to discuss the accuracy of the approximations as well as the advantages and the disadvantages of both methods. It is shown to which extent the results fulfill physical requirements for the observables and which properties of the methods lead to unphysical results. © 2017, EDP Sciences, SIF, Springer-Verlag Berlin Heidelberg.view abstract 10.1140/epjb/e2017-80063-2 **Effects of interactions on dynamic correlations of hard-core bosons at finite temperatures**

Fauseweh, B. and Uhrig, G.S.*Physical Review B*96 (2017)We investigate how dynamic correlations of hard-core bosonic excitation at finite temperature are affected by additional interactions besides the hard-core repulsion which prevents them from occupying the same site. We focus especially on dimerized spin systems, where these additional interactions between the elementary excitations, triplons, lead to the formation of bound states, relevant for the correct description of scattering processes. In order to include these effects quantitatively, we extend the previously developed Brückner approach to include also nearest-neighbor (NN) and next-nearest neighbor (NNN) interactions correctly in a low-temperature expansion. This leads to the extension of the scalar Bethe-Salpeter equation to a matrix-valued equation. As an example, we consider the Heisenberg spin ladder to illustrate the significance of the additional interactions on the spectral functions at finite temperature, which are proportional to inelastic neutron scattering rates. © 2017 American Physical Society.view abstract 10.1103/PhysRevB.96.115150 **Efficient algorithms for the dynamics of large and infinite classical central spin models**

Fauseweh, B. and Schering, P. and Hüdepohl, J. and Uhrig, G.S.*Physical Review B*96 (2017)We investigate the time dependence of correlation functions in the central spin model, which describes the electron or hole spin confined in a quantum dot, interacting with a bath of nuclear spins forming the Overhauser field. For large baths, a classical description of the model yields quantitatively correct results. We develop and apply various algorithms in order to capture the long-time limit of the central spin for bath sizes from 1000 to infinitely many bath spins. Representing the Overhauser field in terms of orthogonal polynomials, we show that a carefully reduced set of differential equations is sufficient to compute the spin correlations of the full problem up to very long times, for instance up to 105/JQ where JQ is the natural energy unit of the system. This technical progress renders an analysis of the model with experimentally relevant parameters possible. We benchmark the results of the algorithms with exact data for a small number of bath spins and we predict how the long-time correlations behave for different effective numbers of bath spins. © 2017 American Physical Society.view abstract 10.1103/PhysRevB.96.054415 **Influence of the nuclear Zeeman effect on mode locking in pulsed semiconductor quantum dots**

Beugeling, W. and Uhrig, G.S. and Anders, F.B.*Physical Review B*96 (2017)The coherence of the electron spin in a semiconductor quantum dot is strongly enhanced by mode locking through nuclear focusing, where the synchronization of the electron spin to periodic pulsing is slowly transferred to the nuclear spins of the semiconductor material, mediated by the hyperfine interaction between these. The external magnetic field that drives the Larmor oscillations of the electron spin also subjects the nuclear spins to a Zeeman-like coupling, albeit a much weaker one. For typical magnetic fields used in experiments, the energy scale of the nuclear Zeeman effect is comparable to that of the hyperfine interaction, so that it is not negligible. In this work, we analyze the influence of the nuclear Zeeman effect on mode locking quantitatively. Within a perturbative framework, we calculate the Overhauser-field distribution after a prolonged period of pulsing. We find that the nuclear Zeeman effect can exchange resonant and nonresonant frequencies. We distinguish between models with a single type and with multiple types of nuclei. For the latter case, the positions of the resonances depend on the individual g factors, rather than on the average value. © 2017 American Physical Society.view abstract 10.1103/PhysRevB.96.115303 **Massive spinons in S=1/2 spin chains: Spinon-pair operator representation**

Hafez-Torbati, M. and Uhrig, G.S.*Physical Review B*95 (2017)Spinons are among the generic excitations in one-dimensional spin systems; they can be massless or massive. The quantitative description of massive spinons poses a considerable challenge in spite of various variational approaches. We show that a representation in terms of hopping and Bogoliubov spinon processes, which we call "spinon-pair" operators, and their combination is possible. We refer to such a representation as second quantized form. Neglecting terms which change the number of spinons yields the variational results. Treating the bilinear and quartic terms by continuous unitary transformations leads to considerably improved results. Thus, we provide the proof of principle that systems displaying massive spinons as elementary excitations can be treated in second quantization based on spinon-pair representation. © 2017 American Physical Society.view abstract 10.1103/PhysRevB.95.155136 **Singlet exciton condensation and bond-order-wave phase in the extended Hubbard model**

Hafez-Torbati, M. and Uhrig, G.S.*Physical Review B*96 (2017)The competition of interactions implies the compensation of standard mechanisms, which leads to the emergence of exotic phases between conventional phases. The extended Hubbard model (EHM) is a fundamental example for the competition of the local Hubbard interaction and the nearest-neighbor density-density interaction, which at half-filling and in one dimension leads to a bond-order wave (BOW) between a charge-density wave (CDW) and a quasi-long-range order Mott insulator. We study the full momentum-resolved excitation spectrum of the one-dimensional EHM in the CDW phase, and we clarify the relation between different elementary energy gaps. We show that the CDW-to-BOW transition is driven by the softening of a singlet exciton at momentum π. The BOW is realized as the condensate of this singlet exciton. © 2017 American Physical Society.view abstract 10.1103/PhysRevB.96.125129 **Tunable edge states and their robustness towards disorder**

Malki, M. and Uhrig, G.S.*Physical Review B*95 (2017)The interest in the properties of edge states in Chern insulators and in Z2 topological insulators has increased rapidly in recent years. We present calculations on how to influence the transport properties of chiral and helical edge states by modifying the edges in the Haldane and in the Kane-Mele model. The Fermi velocity of the chiral edge states becomes direction dependent as does the spin-dependent Fermi velocity of the helical edge states. Additionally, we explicitly investigate the robustness of edge states against local disorder. The edge states can be reconstructed in the Brillouin zone in the presence of disorder. The influence of the width and of the length of the system is studied as well as the dependence of the edge states on the strength of the disorder. © 2017 American Physical Society.view abstract 10.1103/PhysRevB.95.235118 **Coupling of Higgs and Leggett modes in non-equilibrium superconductors**

Krull, H. and Bittner, N. and Uhrig, G.S. and Manske, D. and Schnyder, A.P.*Nature Communications*7 (2016)In equilibrium systems amplitude and phase collective modes are decoupled, as they are mutually orthogonal excitations. The direct detection of these Higgs and Leggett collective modes by linear-response measurements is not possible, because they do not couple directly to the electromagnetic field. In this work, using numerical exact simulations we show for the case of two-gap superconductors, that optical pump-probe experiments excite both Higgs and Leggett modes out of equilibrium. We find that this non-adiabatic excitation process introduces a strong interaction between the collective modes, which is absent in equilibrium. Moreover, we propose a type of pump-probe experiment, which allows to probe and coherently control the Higgs and Leggett modes, and thus the order parameter directly. These findings go beyond two-band superconductors and apply to general collective modes in quantum materials.view abstract 10.1038/ncomms11921 **Increased coherence time in narrowed bath states in quantum dots**

Gravert, L.B. and Lorenz, P. and Nase, C. and Stolze, J. and Uhrig, G.S.*Physical Review B - Condensed Matter and Materials Physics*94 (2016)We study the influence of narrowed distributions of the nuclear Overhauser field on the decoherence of a central electron spin in quantum dots. We describe the spin dynamics in quantum dots by the central spin model. We use analytic solutions for uniform couplings and the time dependent density-matrix renormalization group (tDMRG) for nonuniform couplings. With these tools we calculate the dynamics of the central spin for large baths of nuclear spins with or without external magnetic field applied to the central spin. The focus of our study is the influence of initial mixtures with narrowed distributions of the Overhauser field and of applied magnetic fields on the decoherence of the central spin. © 2016 American Physical Society.view abstract 10.1103/PhysRevB.94.094416 **Magnetic excitations in the S= 12 antiferromagnetic-ferromagnetic chain compound BaCu2 V2 O8 at zero and finite temperature**

Klyushina, E.S. and Tiegel, A.C. and Fauseweh, B. and Islam, A.T.M.N. and Park, J.T. and Klemke, B. and Honecker, A. and Uhrig, G.S. and Manmana, S.R. and Lake, B.*Physical Review B - Condensed Matter and Materials Physics*93 (2016)Unlike most quantum systems which rapidly become incoherent as temperature is raised, strong correlations persist at elevated temperatures in S=12 dimer magnets, as revealed by the unusual asymmetric line shape of their excitations at finite temperatures. Here, we quantitatively explore and parametrize the strongly correlated magnetic excitations at finite temperatures using high-resolution inelastic neutron scattering of the model compound BaCu2V2O8 which we show to be an alternating antiferromagnetic-ferromagnetic spin-12 chain. Comparison to state of the art computational techniques shows excellent agreement over a wide temperature range. Our findings hence demonstrate the possibility to quantitatively predict coherent behavior at elevated temperatures in quantum magnets. © 2016 American Physical Society.view abstract 10.1103/PhysRevB.93.241109 **Minimal model for the frustrated spin ladder system BiCu2PO6**

Splinter, L. and Drescher, N.A. and Krull, H. and Uhrig, G.S.*Physical Review B - Condensed Matter and Materials Physics*94 (2016)To establish the microscopic model of the compound BiCu2PO6 is a challenging task. Inelastic neutron scattering experiments showed that the dispersion of this material is nondegenerate suggesting the existence of anisotropic interactions. Here we present a quantitative description of the excitation spectrum for BiCu2PO6 on the one-particle level. The solution of the isotropic frustrated spin ladder by continuous unitary transformations is the starting point of our approach. Further couplings such as isotropic interladder couplings and anisotropic interactions are included on the mean-field level. Our aim is to establish a minimal model built on the symmetry-allowed interactions and to find a set of parameters which allows us to describe the low-energy part of the dispersion without assuming unrealistic couplings. © 2016 American Physical Society.view abstract 10.1103/PhysRevB.94.155115 **Orientational bond and Néel order in the two-dimensional ionic Hubbard model**

Hafez-Torbati, M. and Uhrig, G.S.*Physical Review B - Condensed Matter and Materials Physics*93 (2016)Unconventional phases often occur where two competing mechanisms compensate. An excellent example is the ionic Hubbard model where the alternating local potential δ, favoring a band insulator (BI), competes with the local repulsion U, favoring a Mott insulator (MI). By continuous unitary transformations we derive effective models in which we study the softening of various excitons. The softening signals the instability towards new phases that we describe on the mean-field level. On increasing U from the BI in two dimensions, we find a bond-ordered phase breaking orientational symmetry due to a d-wave component. Then, antiferromagnetic order appears coexisting with the d-wave bond order. Finally, the d-wave order vanishes and a Néel-type MI persists. © 2016 American Physical Society.view abstract 10.1103/PhysRevB.93.195128 **Persisting correlations of a central spin coupled to large spin baths**

Seifert, U. and Bleicker, P. and Schering, P. and Faribault, A. and Uhrig, G.S.*Physical Review B - Condensed Matter and Materials Physics*94 (2016)The decohering environment of a quantum bit is often described by the coupling to a large bath of spins. The quantum bit itself can be seen as a spin S=12 which is commonly called the central spin. The resulting central spin model describes an important mechanism of decoherence. We provide mathematically rigorous bounds for a persisting magnetization of the central spin in this model with and without magnetic field. In particular, we show that there is a well-defined limit of infinite number of bath spins. Only if the fraction of very weakly coupled bath spins tends to 100% does no magnetization persist. © 2016 American Physical Society.view abstract 10.1103/PhysRevB.94.094308 **Quantum model for mode locking in pulsed semiconductor quantum dots**

Beugeling, W. and Uhrig, G.S. and Anders, F.B.*Physical Review B - Condensed Matter and Materials Physics*94 (2016)Quantum dots in GaAs/InGaAs structures have been proposed as a candidate system for realizing quantum computing. The short coherence time of the electronic quantum state that arises from coupling to the nuclei of the substrate is dramatically increased if the system is subjected to a magnetic field and to repeated optical pulsing. This enhancement is due to mode locking: oscillation frequencies resonant with the pulsing frequencies are enhanced, while off-resonant oscillations eventually die out. Because the resonant frequencies are determined by the pulsing frequency only, the system becomes immune to frequency shifts caused by the nuclear coupling and by slight variations between individual quantum dots. The effects remain even after the optical pulsing is terminated. In this work, we explore the phenomenon of mode locking from a quantum mechanical perspective. We treat the dynamics using the central-spin model, which includes coupling to 10-20 nuclei and incoherent decay of the excited electronic state, in a perturbative framework. Using scaling arguments, we extrapolate our results to realistic system parameters. We estimate that the synchronization to the pulsing frequency needs time scales in the order of 1s. © 2016 American Physical Society.view abstract 10.1103/PhysRevB.94.245308 **Time-dependent correlations in quantum magnets at finite temperature**

Fauseweh, B. and Groitl, F. and Keller, T. and Rolfs, K. and Tennant, D.A. and Habicht, K. and Uhrig, G.S.*Physical Review B - Condensed Matter and Materials Physics*94 (2016)In this Rapid Communication we investigate the time dependence of the gap mode of copper nitrate at various temperatures. We combine state-of-the-art theoretical calculations with high precision neutron resonance spin-echo measurements to understand the anomalous decoherence effects found previously in this material. It is shown that the time domain offers a complementary view on this phenomenon, which allows us to directly compare experimental data and theoretical predictions without the need of further intensive data analysis, such as (de)convolution. ©2016 American Physical Society.view abstract 10.1103/PhysRevB.94.180404 **Topologically nontrivial hofstadter bands on the kagome lattice**

Redder, C.H. and Uhrig, G.S.*Physical Review A - Atomic, Molecular, and Optical Physics*93 (2016)We investigate how the multiple bands of fermions on a crystal lattice evolve if a magnetic field is added which does not increase the number of bands. The kagome lattice is studied as generic example for a lattice with loops of three bonds. Finite Chern numbers occur as a nontrivial topological property in the presence of the magnetic field. The symmetries and periodicities as a function of the applied field are discussed. Strikingly, the dispersions of the edge states depend crucially on the precise shape of the boundary. This suggests that suitable design of the boundaries helps to tune physical properties which may even differ between upper and lower edges. Moreover, we suggest a promising gauge to realize this model in optical lattices. © 2016 American Physical Society.view abstract 10.1103/PhysRevA.93.033654 **Tunable and direction-dependent group velocities in topologically protected edge states**

Uhrig, G.S.*Physical Review B - Condensed Matter and Materials Physics*93 (2016)Topological effects continue to fascinate physicists since more than three decades. One of their main applications are high-precision measurements of the resistivity. We propose to make also use of the spatially separated edge states. It is possible to realize strongly direction-dependent group velocities. They can also be tuned over orders of magnitude so that robust and tunable delay lines and interference devices are within reach. © 2016 American Physical Society.view abstract 10.1103/PhysRevB.93.205438 **Effective models for Anderson impurity and Kondo problems from continuous unitary transformations**

Krones, J. and Uhrig, G.S.*Physical Review B - Condensed Matter and Materials Physics*91 (2015)The method of continuous unitary transformations (CUTs) is applied to the Anderson impurity and the Kondo model aiming at the systematic derivation of convergent effective models. If CUTs are applied in a conventional way, diverging differential equations occur. Similar to poor man's scaling, the energy scale, below which the couplings diverge, corresponds to the Kondo temperature TK. We present a way to apply CUTs to the Kondo and to the Anderson impurity model so that no divergences occur but a converged effective low-energy model is derived with small finite parameters at arbitrarily small energies. The ground state corresponds to a bound singlet with a binding energy given by the Kondo temperature TK. © 2015 American Physical Society.view abstract 10.1103/PhysRevB.91.125102 **Effective one-dimensional models from matrix product states**

Keim, F. and Uhrig, G.S.*European Physical Journal B*88 (2015)In this paper we present a method for deriving effective one-dimensional models based on the matrix product state formalism. It exploits translational invariance to work directly in the thermodynamic limit. We show, how a representation of the creation operator of single quasi-particles in both real and momentum space can be extracted from the dispersion calculation. The method is tested for the analytically solvable Ising model in a transverse magnetic field. Properties of the matrix product representation of the creation operator are discussed and validated by calculating the one-particle contribution to the spectral weight. Results are also given for the ground state energy and the dispersion. © 2015, EDP Sciences, SIF, Springer-Verlag Berlin Heidelberg.view abstract 10.1140/epjb/e2015-60188-0 **From gapped excitons to gapless triplons in one dimension**

Hafez-Torbati, M. and Drescher, N.A. and Uhrig, G.S.*European Physical Journal B*88 (2015)Often, exotic phases appear in the phase diagrams between conventional phases. Their elementary excitations are of particular interest. Here, we consider the example of the ionic Hubbard model in one dimension. This model is a band insulator (BI) for weak interaction and a Mott insulator (MI) for strong interaction. In between, a spontaneously dimerized insulator (SDI) occurs which is governed by energetically low-lying charge and spin degrees of freedom. Applying a systematically controlled version of the continuous unitary transformations (CUTs) we are able to determine the dispersions of the elementary charge and spin excitations and of their most relevant bound states on equal footing. The key idea is to start from an externally dimerized system using the relative weak interdimer coupling as small expansion parameter which finally is set to unity to recover the original model. © EDP Sciences, Società Italiana di Fisica, Springer-Verlag 2015.view abstract 10.1140/epjb/e2014-50551-0 **Low-temperature thermodynamics of multiflavored hardcore bosons by the Brückner approach**

Fauseweh, B. and Uhrig, G.S.*Physical Review B - Condensed Matter and Materials Physics*92 (2015)Dynamic correlations of quantum magnets provide valuable information. However, especially at finite temperature, many observations, e.g., by inelastic neutron scattering experiments, are not yet quantitatively understood. Generically, the elementary excitations of gapped quantum magnets are hardcore bosons because no two of them can occupy the same site. The previously introduced diagrammatic Brückner approach dealt with hardcore bosons of a single flavor at finite temperature. Here, this approach is extended to hardcore bosons of several kinds (flavors). The approach based on ladder diagrams is gauged with so far unknown rigorous results for the thermal occupation function of multiflavored hardcore bosons in one dimension with nearest-neighbor hopping. For low temperatures, it works very well. Furthermore, we study to which extent the approach is a conserving approximation. Empirical evidence shows that this is true only in the single-flavor case. © 2015 American Physical Society.view abstract 10.1103/PhysRevB.92.214417 **Roton Minimum as a Fingerprint of Magnon-Higgs Scattering in Ordered Quantum Antiferromagnets**

Powalski, M. and Uhrig, G.S. and Schmidt, K.P.*Physical Review Letters*115 (2015)A quantitative description of magnons in long-range ordered quantum antiferromagnets is presented which is consistent from low to high energies. It is illustrated for the generic S=1/2 Heisenberg model on the square lattice. The approach is based on a continuous similarity transformation in momentum space using the scaling dimension as the truncation criterion. Evidence is found for significant magnon-magnon attraction inducing a Higgs resonance. The high-energy roton minimum in the magnon dispersion appears to be induced by strong magnon-Higgs scattering. © 2015 American Physical Society.view abstract 10.1103/PhysRevLett.115.207202 **Anomalous behavior of control pulses in presence of noise with singular autocorrelation**

Stanek, D. and Fauseweh, B. and Stihl, C. and Pasini, S. and Uhrig, G.S.*Journal of Magnetic Resonance*245 (2014)We report on the anomalous behavior of control pulses for spins under spin-spin relaxation and subject to classical noise with a singular autocorrelation function. This behavior is not detected for noise with analytic autocorrelation functions. The effect is manifest in the different scaling behavior of the deviation of a real pulse to the ideal, instantaneous one. While a standard pulse displays scaling ∝τp1, a first-order refocusing pulse normally shows scaling ∝τp2. But in presence of cusps in the noise autocorrelation the scaling ∝τp3/2 occurs. Cusps in the autocorrelation are characteristic for fast fluctuations in the noise with a spectral density of Lorentzian shape. We prove that the anomalous exponent cannot be avoided; it represents a fundamental limit. On the one hand, this redefines the strategies one has to adopt to design refocusing pulses. On the other hand, the anomalous exponent, if found in experiment, provides important information on the noise properties. © 2014 Elsevier Inc. All rights reserved.view abstract 10.1016/j.jmr.2014.06.009 **Conservation laws protect dynamic spin correlations from decay: Limited role of integrability in the central spin model**

Uhrig, G.S. and Hackmann, J. and Stanek, D. and Stolze, J. and Anders, F.B.*Physical Review B - Condensed Matter and Materials Physics*90 (2014)Mazur's inequality renders statements about persistent correlations possible. We generalize it in a convenient form applicable to any set of linearly independent constants of motion. This approach is used to show rigorously that a fraction of the initial spin correlations persists indefinitely in the isotropic central spin model unless the average coupling vanishes. The central spin model describes a major mechanism of decoherence in a large class of potential realizations of quantum bits. Thus the derived results contribute significantly to the understanding of the preservation of coherence. We will show that persisting quantum correlations are not linked to the integrability of the model but are caused by a finite operator overlap with a finite set of constants of motion. © 2014 American Physical Society.view abstract 10.1103/PhysRevB.90.060301 **Dispersive excitations in one-dimensional ionic Hubbard model**

Hafez Torbati, M. and Drescher, N.A. and Uhrig, G.S.*Physical Review B - Condensed Matter and Materials Physics*89 (2014)A detailed study of the one-dimensional ionic Hubbard model with interaction U is presented. We focus on the band insulating (BI) phase and the spontaneously dimerized insulating (SDI) phase which appears on increasing U. By a recently introduced continuous unitary transformation [H. Krull, Phys. Rev. B 86, 125113 (2012)PRBMDO1098-012110.1103/PhysRevB.86.125113] we are able to describe the system even close to the phase transition from BI to SDI although the bare perturbative series diverges before the transition is reached. First, the dispersion of single fermionic quasiparticles is determined in the full Brillouin zone. Second, we describe the binding phenomena between two fermionic quasiparticles leading to an S=0 and to an S=1 exciton. The latter corresponds to the lowest spin excitation and defines the spin gap which remains finite through the transition from BI to SDI. The former becomes soft at the transition, indicating that the SDI corresponds to a condensate of these S=0 excitons. This view is confirmed by a BCS mean-field theory for the SDI phase. © 2014 American Physical Society.view abstract 10.1103/PhysRevB.89.245126 **Finite-temperature line shapes of hard-core bosons in quantum magnets: A diagrammatic approach tested in one dimension**

Fauseweh, B. and Stolze, J. and Uhrig, G.S.*Physical Review B - Condensed Matter and Materials Physics*90 (2014)The dynamics in quantum magnets can often be described by effective models with bosonic excitations obeying a hard-core constraint. Such models can be systematically derived by renormalization schemes such as continuous unitary transformations or by variational approaches. Even in the absence of further interactions the hard-core constraint makes the dynamics of the hard-core bosons nontrivial. Here, we develop a systematic diagrammatic approach to the spectral properties of hard-core bosons at finite temperature. Starting from an expansion in the density of thermally excited bosons in a system with an energy gap, our approach leads to a summation of ladder diagrams. Conceptually, the approach is not restricted to one dimension, but the one-dimensional case offers the opportunity to gauge the method by comparison to exact results obtained via a mapping to Jordan-Wigner fermions. In particular, we present results for the thermal broadening of single-particle spectral functions at finite temperature. The line shape is found to be asymmetric at elevated temperatures and the bandwidth of the dispersion narrows with increasing temperature. Additionally, the total number of thermally excited bosons is calculated and compared to various approximations and analytic results. Thereby, a flexible approach is introduced that can also be applied to more sophisticated and higher dimensional models. © 2014 American Physical Society.view abstract 10.1103/PhysRevB.90.024428 **From quantum-mechanical to classical dynamics in the central-spin model**

Stanek, D. and Raas, C. and Uhrig, G.S.*Physical Review B - Condensed Matter and Materials Physics*90 (2014)We discuss the semiclassical and classical character of the dynamics of a single spin 1/2 coupled to a bath of noninteracting spins 1/2. On the semiclassical level, we extend our previous approach presented in D. Stanek, C. Raas, and G. S. Uhrig, Phys. Rev. B 88, 155305 (2013)PRBMDO1098-012110.1103/ PhysRevB.88.155305 by the explicit consideration of the conservation of the total spin. On the classical level, we compare the results of the classical equations of motions in absence and presence of an external field to the full quantum result obtained by density-matrix renormalization (DMRG). We show that for large bath sizes and not too low magnetic field the classical dynamics, averaged over Gaussian distributed initial spin vectors, agrees quantitatively with the quantum-mechanical one. This observation paves the way for an efficient approach for certain parameter regimes. © 2014 American Physical Society.view abstract 10.1103/PhysRevB.90.064301 **Interaction quenches in the two-dimensional fermionic Hubbard model**

Hamerla, S.A. and Uhrig, G.S.*Physical Review B - Condensed Matter and Materials Physics*89 (2014)The generic nonequilibrium evolution of a strongly interacting fermionic system is studied. For strong quenches, a collective collapse-and-revival phenomenon is found to extend over the whole Brillouin zone. A qualitatively distinct behavior occurs for weak quenches where only weak wiggling occurs. Surprisingly, no evidence for prethermalization is found in the weak-coupling regime. In both regimes, indications for relaxation beyond oscillatory or power-law behavior are found and used to estimate relaxation rates without resorting to a probabilistic ansatz. The relaxation appears to be fastest for intermediate values of the quenched interaction. © 2014 American Physical Society.view abstract 10.1103/PhysRevB.89.104301 **Signatures of nonadiabatic BCS state dynamics in pump-probe conductivity**

Krull, H. and Manske, D. and Uhrig, G.S. and Schnyder, A.P.*Physical Review B - Condensed Matter and Materials Physics*90 (2014)We theoretically study the pump-probe response of nonequilibrium BCS superconductors coupled to optical phonons. For ultrashort pump pulses a nonadiabatic regime emerges, which is characterized by oscillations of the superconducting order parameter as well as by the generation of coherent phonons. Using the density-matrix formalism, we compute the pump-probe response in the nonadiabatic regime of the coupled Bogoliubov quasiparticle-phonon system and determine the signatures of the order parameter and the phonon oscillations in the pump-probe conductivity. We find that the nonadiabatic dynamics of the BCS superconductor reflects itself in oscillations of the pump-probe response as functions of delay time t between pump and probe pulses. We argue that from the analysis of this oscillatory behavior both frequency and decay time of the algebraically decaying order-parameter oscillations can be inferred. Similarly, the coherent phonons are evidenced in the pump-probe conductivity by oscillations with the frequency of the phonons. Remarkably, we find that the oscillatory response in the pump-probe conductivity is resonantly enhanced when the frequency of the order-parameter oscillations is tuned to the phonon energy. © 2014 American Physical Society.view abstract 10.1103/PhysRevB.90.014515 **Dynamical transition in interaction quenches of the one-dimensional Hubbard model**

Hamerla, S.A. and Uhrig, G.S.*Physical Review B - Condensed Matter and Materials Physics*87 (2013)We show that the nonequilibrium time evolution after interaction quenches in the one-dimensional, integrable Hubbard model exhibits a dynamical transition in the half-filled case. This transition ceases to exist upon doping. Our study is based on systematically extended equations of motion. Thus it is controlled for small and moderate times; no relaxation effects are neglected. Remarkable similarities to the quench dynamics in the infinite-dimensional Hubbard model are found, suggesting that dynamical transitions are a general feature of quenches in such models. © 2013 American Physical Society.view abstract 10.1103/PhysRevB.87.064304 **Dynamics and decoherence in the central Spin model in the low-field limit**

Stanek, D. and Raas, C. and Uhrig, G.S.*Physical Review B - Condensed Matter and Materials Physics*88 (2013)We present a combination of analytic calculations and a powerful numerical method for large spin baths in the low-field limit. The hyperfine interaction between the central spin and the bath is fully captured by the density matrix renormalization group. The adoption of the density matrix renormalization group for the central spin model is presented and a proper method for calculating the real-time evolution at infinite temperature is identified. In addition, we study to which extent a semiclassical model, where a quantum spin-1/2 interacts with a bath of classical Gaussian fluctuations, can capture the physics of the central spin model. The model is treated by average Hamiltonian theory and by numerical simulation. © 2013 American Physical Society.view abstract 10.1103/PhysRevB.88.155305 **Multiparticle spectral properties in the transverse field Ising model by continuous unitary transformations**

Fauseweh, B. and Uhrig, G.S.*Physical Review B - Condensed Matter and Materials Physics*87 (2013)The one-dimensional transverse field Ising model is solved by continuous unitary transformations in the high-field limit. A high accuracy is reached due to the closure of the relevant algebra of operators, which we call string operators. The closure is related to the possibility to map the model by Jordan-Wigner transformation to noninteracting fermions, but it is proven without referring to this mapping. The effective model derived by the continuous unitary transformations is used to compute the contributions of one, two, and three elementary excitations to the diagonal dynamic structure factors. The three-particle contributions have, so far, not been addressed analytically, except close to the quantum critical point. © 2013 American Physical Society.view abstract 10.1103/PhysRevB.87.184406 **One-dimensional fermionic systems after interaction quenches and their description by bosonic field theories**

Hamerla, S.A. and Uhrig, G.S.*New Journal of Physics*15 (2013)We study the time evolution of two fermionic one-dimensional models (spinless fermions with nearest-neighbor repulsion and the Hubbard model) exposed to an interaction quench for short and moderate times. The method used to calculate the time dependence is a semi-numerical approach based on the Heisenberg equation of motion. We compare the results of this approach with the results obtained by bosonization implying power law behavior. Indeed, we find that power laws describe our results well, but our results raise the issue of which exponents occur. For spinless fermions, it seems that the Tomonaga-Luttinger parameters work well, which also describe the equilibrium low-energy physics. But for the Hubbard model this is not the case. Instead, we find that exponents from the bosonization around the initial state work well. Finally, we discuss what can be expected for the long-time behavior. © IOP Publishing and Deutsche Physikalische Gesellschaft.view abstract 10.1088/1367-2630/15/7/073012 **Varied perturbation theory for the dispersion dip in the two-dimensional Heisenberg quantum antiferromagnet**

Uhrig, G.S. and Majumdar, K.*European Physical Journal B*86 (2013)We study the roton-like dip in the magnon dispersion at the boundary of the Brillouin zone in the isotropic S = 1/2 Heisenberg quantum antiferromagnet. This high-energy feature is sometimes seen as indication of a fractionalization of the magnons to spinons. In this article, we provide evidence that the description of the dip in terms of magnons can be improved significantly by applying more advanced evaluation schemes. In particular, we illustrate the usefulness of the application of the principle of minimal sensitivity in varied perturbation theory. Thereby, we provide an example for the application of this approach to an extended condensed matter problem governed by correlations which can trigger analogous investigations for many other systems. © 2013 EDP Sciences, Società Italiana di Fisica, Springer-Verlag.view abstract 10.1140/epjb/e2013-40159-3 **Effects of ring exchange interaction on the Néel phase of two-dimensional, spatially anisotropic, frustrated Heisenberg quantum antiferromagnet**

Majumdar, K. and Furton, D. and Uhrig, G.S.*Physical Review B - Condensed Matter and Materials Physics*85 (2012)Higher-order quantum effects on the magnetic phase diagram induced by four-spin ring exchange on plaquettes are investigated for a two-dimensional quantum antiferromagnet with S=1/2. Spatial anisotropy and frustration are allowed for. Using a perturbative spin-wave expansion up to second order in 1/S we obtain the spin-wave energy dispersion, sublattice magnetization, and magnetic phase diagram. We find that for substantial four-spin ring exchange the quantum fluctuations are stronger than in the standard Heisenberg model. A moderate amount of four-spin ring exchange couplings stabilizes the ordered antiferromagnetic Néel state while a large amount renders it unstable. Comparison with inelastic neutron-scattering data for cuprates points toward a moderate ring exchange coupling of 27 to 29% of the nearest-neighbor exchange coupling. © 2012 American Physical Society.view abstract 10.1103/PhysRevB.85.144420 **Enhanced perturbative continuous unitary transformations**

Krull, H. and Drescher, N.A. and Uhrig, G.S.*Physical Review B - Condensed Matter and Materials Physics*86 (2012)Unitary transformations are an essential tool for the theoretical understanding of many systems by mapping them to simpler effective models. A systematically controlled variant to perform such a mapping is a perturbative continuous unitary transformation (pCUT) among others. So far, this approach required an equidistant unperturbed spectrum. Here, we pursue two goals: First, we extend its applicability to nonequidistant spectra with the particular focus on an efficient derivation of the differential flow equations, which define the enhanced perturbative continuous unitary transformation (epCUT). Second, we show that the numerical integration of the flow equations yields a robust scheme to extract data from the epCUT. The method is illustrated by the perturbation of the harmonic oscillator with a quartic term and of the two-leg spin ladders in the strong-rung-coupling limit for uniform and alternating rung couplings. The latter case provides an example of perturbation around a nonequidistant spectrum. © 2012 American Physical Society.view abstract 10.1103/PhysRevB.86.125113 **Frequency-modulated pulses for quantum bits coupled to time-dependent baths**

Fauseweh, B. and Pasini, S. and Uhrig, G.S.*Physical Review A - Atomic, Molecular, and Optical Physics*85 (2012)We consider the coherent control of a quantum bit by the use of short pulses with finite duration τ p. By shaping the pulse, we perturbatively decouple the dynamics of the bath from the dynamics of the quantum bit during the pulse. Such shaped pulses provide single quantum bit gates robust against decoherence which are useful for quantum-information processing. We extend previous results in two ways: (i) we treat frequency-modulated pulses and (ii) we pass from time-independent baths to analytically time-dependent baths. First- and second-order solutions for π and π/2 pulses are presented. They are useful in experiments where amplitude modulation is difficult to realize. © 2012 American Physical Society.view abstract 10.1103/PhysRevA.85.022310 **Perfect state transfer in XX chains induced by boundary magnetic fields**

Linneweber, T. and Stolze, J. and Uhrig, G.S.*International Journal of Quantum Information*10 (2012)A recent numerical study of short chains found near-perfect quantum state transfer between the boundary sites of a spin-1/2 XX chain if a sufficiently strong magnetic field acts on these sites. We show that the phenomenon is based on a pair of states strongly localized at the boundaries of the system and provide a simple quantitative analytical explanation. © 2012 World Scientific Publishing Company.view abstract 10.1142/S0219749912500293 **Erratum: Exact results on dynamical decoupling by π pulses in quantum information processes (New Journal of Physics (2008) 10 (083024))**

Uhrig, G.S.*New Journal of Physics*13 (2011)view abstract 10.1088/1367-2630/13/5/059504 **Erratum: Keeping a quantum bit alive by optimized π-pulse sequences (Physical Review Letters (2007) 98 (100504))**

Uhrig, G.S.*Physical Review Letters*106 (2011)view abstract 10.1103/PhysRevLett.106.129901 **High-order coherent control sequences of finite-width pulses**

Pasini, S. and Karbach, P. and Uhrig, G.S.*EPL*96 (2011)The performance of sequences of designed pulses of finite length τ is analyzed for a bath of spins and it is compared with that of sequences of ideal, instantaneous pulses. The degree of the design of the pulse strongly affects the performance of the sequences. Non-equidistant, adapted sequences of pulses, which equal instantaneous ones up to O(τ 3), outperform equidistant or concatenated sequences. Moreover, they do so at low energy cost which grows only logarithmically with the number of pulses, in contrast to standard pulses with linear growth. © 2011 Europhysics Letters Association.view abstract 10.1209/0295-5075/96/10003 **Hole dispersions for antiferromagnetic spin-1/2 two-leg ladders by self-similar continuous unitary transformations**

Duffe, S. and Uhrig, G.S.*European Physical Journal B*84 (2011)The hole-doped antiferromagnetic spin-1/2 two-leg ladder is an important model system for the high-T c superconductors based on cuprates. Using the technique of self-similar continuous unitary transformations we derive effective Hamiltonians for the charge motion in these ladders. The key advantage of this technique is that it provides effective models explicitly in the thermodynamic limit. A real space restriction of the generator of the transformation allows us to explore the experimentally relevant parameter space. From the effective Hamiltonians we calculate the dispersions for single holes. Further calculations will enable the calculation of the interaction of two holes so that a handle of Cooper pair formation is within reach. © 2011 EDP Sciences, SIF, Springer-Verlag Berlin Heidelberg.view abstract 10.1140/epjb/e2011-20150-x **Kinks in the electronic dispersion of the Hubbard model away from half filling**

Grete, P. and Schmitt, S. and Raas, C. and Anders, F.B. and Uhrig, G.S.*Physical Review B - Condensed Matter and Materials Physics*84 (2011)We study kinks in the electronic dispersion of a generic strongly correlated system by dynamic mean-field theory (DMFT). The focus is on doped systems away from particle-hole symmetry where valence fluctuations matter potentially. Three different algorithms are compared to asses their strengths and weaknesses, as well as to clearly distinguish physical features from algorithmic artifacts. Our findings extend a view previously established for half-filled systems where kinks reflect the coupling of the fermionic quasiparticles to emergent collective modes, which are identified here as spin fluctuations. Kinks are observed when strong spin fluctuations are present and, additionally, a separation of energy scales for spin and charge excitations exists. Both criteria are met by strongly correlated systems close to a Mott-insulator transition. The energies of the kinks and their doping dependence fit well to the kinks in the cuprates, which is surprising in view of the spatial correlations neglected by DMFT. © 2011 American Physical Society.view abstract 10.1103/PhysRevB.84.205104 **Microscopic model for Bose-Einstein condensation and quasiparticle decay**

Fischer, T. and Duffe, S. and Uhrig, G.S.*EPL*96 (2011)Sufficiently dimerized quantum antiferromagnets display elementary S=1 excitations, triplon quasiparticles, protected by a gap at low energies. At higher energies, the triplons may decay into two or more triplons. A strong enough magnetic field induces Bose-Einstein condensation of triplons. For both phenomena the compound IPA-CuCl 3 is an excellent model system. Nevertheless no quantitative model was determined so far despite numerous studies. Recent theoretical progress allows us to analyse data of inelastic neutron scattering (INS) and of magnetic susceptibility to determine the four magnetic couplings J 1≈- 2.3 meV, J 2≈1.2 meV, J 3≈2.9 meV and J 4≈- 0.3 meV. These couplings determine IPA-CuCl 3 as system of coupled asymmetric S=1/2 Heisenberg ladders quantitatively. The magnetic field dependence of the lowest modes in the condensed phase as well as the temperature dependence of the gap without magnetic field corroborate this microscopic model. © 2011 Europhysics Letters Association.view abstract 10.1209/0295-5075/96/47001 **Rigorous performance bounds for quadratic and nested dynamical decoupling**

Xia, Y. and Uhrig, G.S. and Lidar, D.A.*Physical Review A - Atomic, Molecular, and Optical Physics*84 (2011)We present rigorous performance bounds for the quadratic dynamical decoupling pulse sequence which protects a qubit from general decoherence, and for its nested generalization to an arbitrary number of qubits. Our bounds apply under the assumptions of instantaneous pulses and of bounded perturbing environment and qubit-environment Hamiltonians such as those realized by baths of nuclear spins in quantum dots. We prove that if the total sequence time is fixed then the trace-norm distance between the unperturbed and protected system states can be made arbitrarily small by increasing the number of applied pulses. © 2011 American Physical Society.view abstract 10.1103/PhysRevA.84.062332 **Self-consistent spin-wave theory for a frustrated Heisenberg model with biquadratic exchange in the columnar phase and its application to iron pnictides**

Stanek, D. and Sushkov, O.P. and Uhrig, G.S.*Physical Review B - Condensed Matter and Materials Physics*84 (2011)Recent neutron scattering studies revealed the three-dimensional character of the magnetism in the iron pnictides and a strong anisotropy between the exchange perpendicular and parallel to the spin stripes. We extend studies of the J1-J2-Jc Heisenberg model with S=1 using self-consistent spin-wave theory. A discussion of two scenarios for the instability of the columnar phase is provided. The relevance of a biquadratic exchange term between in-plane nearest neighbors is discussed. We introduce mean-field decouplings for biquadratic terms using the Dyson-Maleev and the Schwinger boson representation. Remarkably their respective mean-field theories do not lead to the same results, even at zero temperature. They are gauged in the Néel phase in comparison to exact diagonalization and series expansion. The J1-J2-Jc model is analyzed under the influence of the biquadratic exchange Jbq and a detailed description of the staggered magnetization and of the magnetic excitations is given. The biquadratic exchange increases the renormalization of the in-plane exchange constants which enhances the anisotropy between the exchange parallel and perpendicular to the spin stripes. Applying the model to iron pnictides, it is possible to reproduce the spin-wave dispersion for CaFe2As 2 in the direction perpendicular to the spin stripes and perpendicular to the planes. Discrepancies remain in the direction parallel to the spin stripes which can be resolved by passing from S=1 to S=3/2orS=2. In addition, results for the dynamical structure factor within the self-consistent spin-wave theory are provided. © 2011 American Physical Society.view abstract 10.1103/PhysRevB.84.064505 **Symmetry-enhanced performance of dynamical decoupling**

Pasini, S. and Uhrig, G.S.*Physical Review A - Atomic, Molecular, and Optical Physics*84 (2011)We consider a system with general decoherence and a quadratic dynamical decoupling sequence (QDD) for the coherence control of a qubit coupled to a bath of spins. We investigate the influence of the geometry and of the initial conditions of the bath on the performance of the sequence. The overall performance is quantified by a distance norm d. It is expected that d scales with τ, the total duration of the sequence, as τmin{N x ,Nz }+1, where N x and Nz are the number of pulses of the outer and of the inner sequence, respectively. We show both numerically and analytically that the state of the bath can boost the performance of QDD under certain conditions: The scaling of QDD for a given number of pulses can be enhanced by a factor of 2 if the bath is prepared in a highly symmetric state and if the system Hamiltonian is SU(2) invariant. © 2011 American Physical Society.view abstract 10.1103/PhysRevA.84.042336 **Three-dimensional generalization of the J 1-J 2 Heisenberg model on a square lattice and role of the interlayer coupling J c**

Holt, M. and Sushkov, O.P. and Stanek, D. and Uhrig, G.S.*Physical Review B - Condensed Matter and Materials Physics*83 (2011)A possibility to describe magnetism in the iron pnictide parent compounds in terms of the two-dimensional frustrated Heisenberg J 1-J 2 model has been actively discussed recently. However, recent neutron-scattering data have shown that the pnictides have a relatively large spin-wave dispersion in the direction perpendicular to the planes. This indicates that the third dimension is very important. Motivated by this observation we study the J 1-J 2-J c model that is the three-dimensional generalization of the J 1-J 2 Heisenberg model for S=1/2 and S=1. Using self-consistent spin-wave theory we present a detailed description of the staggered magnetization and magnetic excitations in the collinear state. We find that the introduction of the interlayer coupling J c suppresses the quantum fluctuations and strengthens the long-range ordering. In the J 1-J 2-J c model, we find two qualitatively distinct scenarios for how the collinear phase becomes unstable on increasing J 1. Either the magnetization or one of the spin-wave velocities vanishes. For S=1/2 renormalization due to quantum fluctuations is significantly stronger than for S=1, in particular close to the quantum phase transition. Our findings for the J 1-J 2-J c model are of general theoretical interest; however, the results show that it is unlikely that the model is relevant to undoped pnictides. © 2011 American Physical Society.view abstract 10.1103/PhysRevB.83.144528 **Truncation errors in self-similar continuous unitary transformations**

Drescher, N.A. and Fischer, T. and Uhrig, G.S.*European Physical Journal B*79 (2011)Effects of truncation in self-similar continuous unitary transformations (S-CUT) are estimated rigorously. We find a formal description via an inhomogeneous flow equation. In this way, we are able to quantify truncation errors within the framework of the S-CUT and obtain rigorous error bounds for the ground state energy and the highest excited level. These bounds can be lowered exploiting symmetries of the Hamiltonian. We illustrate our approach with results for a toy model of two interacting hard-core bosons and the dimerized S = 1/2 Heisenberg chain. © 2010 EDP Sciences, SIF, Springer-Verlag Berlin Heidelberg.view abstract 10.1140/epjb/e2010-10723-6 **Adapted continuous unitary transformation to treat systems with quasi-particles of finite lifetime**

Fischer, T. and Duffe, S. and Uhrig, G.S.*New Journal of Physics*12 (2010)An improved generator for continuous unitary transformations is introduced to describe systems with unstable quasi-particles. Its general properties are derived and discussed. To illustrate this approach we investigate the asymmetric antiferromagnetic spin-1/2 Heisenberg ladder, which allows for spontaneous triplon decay. We present results for the low-energy spectrum and the momentum resolved spectral density of this system. In particular, we show the resonance behavior of the decaying triplon explicitly. © IOP Publishing Ltd and Deutsche Physikalische Gesellschaft.view abstract 10.1088/1367-2630/12/3/033048 **Derivation of the t-J model for finite doping**

Hamerla, S.A. and Duffe, S. and Uhrig, G.S.*Physical Review B - Condensed Matter and Materials Physics*82 (2010)Mapping complex problems to simpler effective models is a key tool in theoretical physics. One important example in the realm of strongly correlated fermionic systems is the mapping of the Hubbard model to a t-J model which is appropriate for the treatment of doped Mott insulators. Charge fluctuations across the charge gap are eliminated. So far the derivation of the t-J model is only known at half filling or in its immediate vicinity. Here we present the necessary conceptual advancement to treat finite doping. The results for the ensuing coupling constants are presented. Technically, the extended derivation relies on self-similar continuous unitary transformations and normal-ordering relative to a doped reference ensemble. The range of applicability of the derivation of t-J model is determined as function of the doping δ and the ratio bandwidth W over interaction U. © 2010 The American Physical Society.view abstract 10.1103/PhysRevB.82.235117 **Efficient coherent control by sequences of pulses of finite duration**

Uhrig, G.S. and Pasini, S.*New Journal of Physics*12 (2010)Reliable long-time storage of arbitrary quantum states is a key element of quantum information processing. In order to dynamically decouple a spin or quantum bit from a dephasing environment by non-instantaneous pulses, we introduce an optimized sequence of N control π pulses that are realistic in the sense that they have a finite duration and a finite amplitude. We show that optimized dynamical decoupling is still applicable and that higher-order decoupling can be reached if shaped pulses are implemented. The sequence suppresses decoherence up to the order script O sign (TN+1) + script O sign (τmx M), with T being the total duration of the sequence and τmx the maximum length of the pulses. The exponent Mεℕ depends on the shape of the pulse. Based on existing experiments, a concrete setup for the verification of the properties of the advocated sequence is proposed. © IOP Publishing Ltd and Deutsche Physikalische Gesellschaft.view abstract 10.1088/1367-2630/12/4/045001 **Field-induced Tomonaga-Luttinger liquid phase of a two-leg spin-1/2 ladder with strong leg interactions**

Hong, T. and Kim, Y.H. and Hotta, C. and Takano, Y. and Tremelling, G. and Turnbull, M.M. and Landee, C.P. and Kang, H.-J. and Christensen, N.B. and Lefmann, K. and Schmidt, K.P. and Uhrig, G.S. and Broholm, C.*Physical Review Letters*105 (2010)We study the magnetic-field-induced quantum phase transition from a gapped quantum phase that has no magnetic long-range order into a gapless phase in the spin-1/2 ladder compound bis(2,3-dimethylpyridinium) tetrabromocuprate (DIMPY). At temperatures below about 1a K, the specific heat in the gapless phase attains an asymptotic linear temperature dependence, characteristic of a Tomonaga-Luttinger liquid. Inelastic neutron scattering and the specific heat measurements in both phases are in good agreement with theoretical calculations, demonstrating that DIMPY is the first model material for an S=1/2 two-leg spin ladder in the strong-leg regime. © 2010 The American Physical Society.view abstract 10.1103/PhysRevLett.105.137207 **Optimized dynamical decoupling for power-law noise spectra**

Pasini, S. and Uhrig, G.S.*Physical Review A - Atomic, Molecular, and Optical Physics*81 (2010)We analyze the suppression of decoherence by means of dynamical decoupling in the pure-dephasing spin-boson model for baths with power law spectra. The sequence of ideal π pulses is optimized according to the power of the bath. We expand the decoherence function and separate the canceling divergences from the relevant terms. The proposed sequence is chosen to be the one minimizing the decoherence function. By construction, it provides the best performance. We analytically derive the conditions that must be satisfied. The resulting equations are solved numerically. The solutions are very close to the Carr-Purcell-Meiboom-Gill sequence for a soft cutoff of the bath while they approach the Uhrig dynamical-decoupling sequence as the cutoff becomes harder. © 2010 The American Physical Society.view abstract 10.1103/PhysRevA.81.012309 **Optimized dynamical decoupling for time-dependent Hamiltonians**

Pasini, S. and Uhrig, G.S.*Journal of Physics A: Mathematical and Theoretical*43 (2010)The validity of optimized dynamical decoupling (DD) is extended to analytically time-dependent Hamiltonians. As long as an expansion in time is possible, the time dependence of the initial Hamiltonian does not affect the efficiency of optimized dynamical decoupling (UDD, Uhrig DD). This extension provides the analytic basis for (i) applying UDD to effective Hamiltonians in time-dependent reference frames, for instance in the interaction picture of fast modes and for (ii) its application in hierarchical DD schemes with π pulses about two perpendicular axes in spin space to suppress general decoherence, i.e. longitudinal relaxation and dephasing. © 2010 IOP Publishing Ltd.view abstract 10.1088/1751-8113/43/13/132001 **Rigorous bounds for optimal dynamical decoupling**

Uhrig, G.S. and Lidar, D.A.*Physical Review A - Atomic, Molecular, and Optical Physics*82 (2010)We present rigorous performance bounds for the optimal dynamical decoupling pulse sequence protecting a quantum bit (qubit) against pure dephasing. Our bounds apply under the assumption of instantaneous pulses and of bounded perturbing environment and qubit-environment Hamiltonians such as those realized by baths of nuclear spins in quantum dots. We show that if the total sequence time is fixed the optimal sequence can be used to make the distance between the protected and unperturbed qubit states arbitrarily small in the number of applied pulses. If, on the other hand, the minimum pulse interval is fixed and the total sequence time is allowed to scale with the number of pulses, then longer sequences need not always be advantageous. The rigorous bound may serve as a testbed for approximate treatments of optimal decoupling in bounded models of decoherence. © 2010 The American Physical Society.view abstract 10.1103/PhysRevA.82.012301 **Vertex corrections in the dynamic structure factor in spin ladders**

Exius, I. and Schmidt, K.P. and Lake, B. and Tennant, D.A. and Uhrig, G.S.*Physical Review B - Condensed Matter and Materials Physics*82 (2010)We combine the results of perturbative continuous unitary transformations with a mean-field calculation to determine the evolution of the single-mode, i.e., one-triplon, contribution to the dynamic structure factor of a two-leg S=1/2 ladder on increasing temperature from zero to a finite value. The temperature dependence is induced by two effects: (i) no triplon can be excited on a rung where a thermally activated triplon is present and (ii) conditional excitation processes take place if a thermally activated triplon is present. Both effects diminish the one-triplon spectral weight upon heating. It is shown that the second effect is the dominant vertex correction in the calculation of the dynamic structure factor. The matrix elements describing the conditional triplon excitation in the two-leg Heisenberg ladder with additional four-spin ring exchange are calculated perturbatively up to order 9. The calculated results are compared to those of an inelastic neutron scattering experiment on the cuprate-ladder compound La4 Sr10 Cu24 O41 showing convincing agreement for established values of the exchange constants. © 2010 The American Physical Society.view abstract 10.1103/PhysRevB.82.214410

#### antiferromagnetic materials

#### ferromagnetism

#### magnetism