Korrelationstage 2017

The Kitaev honeycomb model is arguably one of the most influential examples of a topologically ordered phase of matter. At the heart of the this model is the Kitaev interaction, which is of Ising type, but where the exchange easy-axis depends on the bond direction. It is one of the few highly frustrated spin models that is exactly solvable and, thus, has shaped our understanding of quantum spin liquid phases in general. In recent years, it has been shown that Kitaev interactions occur naturally in certain transition metal compounds, which are commonly referred to as Kitaev materials. An important hallmark of these systems is the surprising variety of quantum spin liquids that can be realized — in particular in three spatial dimensions. The richness of the theoretical model combined with recent breakthroughs in material synthesis have lead to a rapidly growing field which is marked by the strong interplay of theory and experiment. In this talk, we’ll give an overview of the physics of three-dimensional Kitaev spin liquids, identify hallmarks of topological order and discuss how these may be relevant for the materials.

Unlike conventional magnets where the magnetic moments are partially or completely static in the ground state, in a quantum spin liquid they remain in collective motion down to the lowest temperatures. The importance of this state is that it is coherent and highly entangled without breaking local symmetries. Such phenomena is usually sought in simple lattices where antiferromagnetic interactions and/or anisotropies favoring specific alignments of the magnetic moments, are frustrated by lattice geometries incompatible with such order. Despite an extensive search among such compounds, experimental realizations remain very few. Here we investigate the new spin-1/2 magnet, Ca10Cr7O28, which has a novel unexplored lattice with several isotropic interactions consisting of strong ferromagnetic and weaker antiferromagnetic couplings. Despite its unconventional structure and Hamiltonian, we show experimentally that it displays all the features expected of a quantum spin liquid. Bulk properties measurements, neutron scattering and muon spin relaxation reveal coherent spin dynamics in the ground state, the complete absence of static magnetism and diffuse spinon excitations. Pseudo-Fermion renormalization group calculations verify that the Hamiltonian of Ca10Cr7O28 supports a dynamical ground state which furthermore is robust to significant variations of the exchange constants.

We theoretically investigate the magnetic properties of the bilayer-kagome spin-liquid candidate $Ca_{10}Cr_7O_{28}$. Taking the experimentally observed exchange couplings as an input, we apply the pseudo-fermion functional renormalization group (PFFRG) method to calculate the spin-structure factor and magnetic susceptibility. In agreement with experiments, the temperature dependence of the susceptibility indicates a non-magnetic ground state. We further find qualitative agreement between the calculated and measured spin-structure factors, particularly, our simulations reproduce the characteristic ring-like correlation profile in momentum space which can be interpreted as a signature of molten 120 degree Neel order. By tuning the model parameters away from those realized in $Ca_{10}Cr_7O_{28}$ we show that the spin-liquid phase is of remarkable stability that is rooted in a hierarchy of different frustration and fluctuation effects.

Heavy transition metals ($5d$) and rare-earth atoms ($4f$) entail strong spin-orbit coupling that renders magnetic interactions anisotropic. This creates new mechanisms of magnetic frustration, which can give rise to quantum spin-liquid behavior at low temperatures. In this contribution, I will present recent experimental results on two quantum spin-liquid candidates, Ba$_3$InIr$_2$O$_9$ and YbMgGaO$_4$. YbMgGaO$_4$ entails Yb$^{3+}$ spins arranged on a triangular lattice. From low-temperature specific-heat measurements the absence of a spin gap is inferred, and the T^(2/3) power-law behavior resembles the U(1) quantum spin liquid. $\mu$SR confirms the absence of magnetic ordering or spin freezing down to at least 50 mK. However, inelastic neutron scattering reveals large broadening of crystal-field excitations and other signatures of structural disorder that we ascribe to the random distribution of Mg and Ga in the crystal structure. Ba$_3$InIr$_2$O$_9$ is a mixed-valence compound, where local moments are on Ir-Ir dimers. The interactions between these dimers form triangular and honeycomb geometries simultaneously. Using neutron scattering, NMR, and $\mu$SR we demonstrate that this material is free from structural disorder and shows persistent spin dynamics down to at least 20 mK, with the magnetic susceptibility reaching constant value below 1 K. Spin-lattice relaxation rate follows power-law behavior suggesting the absence of a spin gap

The Heisenberg-Kitaev model and its variants have attracted enormous attention recently, as they are believed to describe the physics proximate to the Kitaev spin liquid as realized in honeycomb-lattice materials such as Na$_2$IrO$_3$ or $\alpha$-RuCl$_3$. We have investigated a variety of these models in applied magnetic fields using semiclassical techniques. The results reveal surprisingly rich phase diagrams, with non-trivial intermediate phases including vortex crystals and other multi-Q states. We discuss possible origins of large magnetic anisotropies as observed experimentally, and we highlight different mechanisms to stabilize zigzag magnetic order and their distinct field response.

Quantum Monte Carlo simulations of frustrated quantum spin systems are usually plagued by a severe sign-problem. However, due to its dependence on the underlying computational basis, it can be feasible to reduce or even avoid the sign-problem by an appropriate local basis choise, which reduces the entanglement between the computational unit cells. Here, we consider in particular the possibility of simulating dimerized quantum spin systems witin a spin-dimer basis world-line formulation. We discuss this simulation scheme and present results for thermodynamic properties of the frustrated spin-half Heisenberg ladder as well as for different frustrated two-dimensional quantum spin systems.

Since the discovery of the quantum Hall effect, the lattice geometry's influence on charged particles in magnetic fields has been the subject of extensive research. Prototypical models such as the non-interacting Harper-Hofstadter model exhibit fractionalization of the Bloch bands with non-trivial topology, manifesting in quantum Hall phases. Ultracold atomic gases with artificial magnetic fields enabled the experimental study of the non-interacting model, while the effect of strong interactions on the band properties remains an open problem. We study the strongly-interacting bosonic Harper-Hofstadter-Mott model using a reciprocal cluster mean-field (RCMF) method, finding several stable and metastable gapped phases with possibly (intrinsic) topological order competing with superfluid phases. We discuss the consequences for experimental realizations and outline strategies to improve the accuracy of the method.

AdS/CFT correspondence and the holographic principle have inspired a new way of looking at interacting quantum field theories in both equilibrium and non-equilibrium. A major challenge for a condensed matter theorist is that they only apply to a very special class of supersymmetric conformal gauge theories in a large-N limit. In this talk I will present a new approach that captures an important aspect of AdS/CFT correspondence for eigenstates of generic many-body Hamiltonians, namely the holographic formulation of entanglement entropies (Ryu-Takayanagi conjecture). I will illustrate this with some explicit calculations for fermionic systems in one and two dimensions. References:\newline S. Kehrein, Preprint arXiv:1703.03925

The field of quantum Hall effect witnessed a huge stimulus when graphene turned out to be a suited host material to observe the integer effect at room temperature and the fractional effect at temperatures that were orders of magnitude higher than accomplished previously. This step is still to come in the field of topological insulators, in particular regarding the quantum spin Hall effect. I will report on a new theoretical scheme to create a systematic framework for high temperature quantum spin Hall effect. We illustrate the idea at the example of a joint experimental/theoretical analysis of Bi/SiC (0001), where by STM we identify the edge state density of states and by ARPES we confirm a bulk gap of 650 meV, nearly two orders of magnitude higher than that of HgTe.

We discuss the influence of electronic correlations on the bulk properties of topological band insulators. In particular, we show how a Hund coupling favoring high spin configurations can provide a generic mechanism for inducing topological insulator phases in multi-band Hubbard models. Interestingly, strong correlations can have qualitative effects on the transition from a trivial band insulator to a topological insulator, ultimately leading to the occurrence of first-order topological quantum phase transitions.

Tensor network states, and in particular projected entangled pair states, play an important role in the description of strongly correlated quantum lattice systems. They do not only serve as variational states in numerical simulation methods, but also provide a framework for classifying phases of quantum matter and capture notions of topological order in a stringent and rigorous language. The rapid development in this field for spin models and bosonic systems has not yet been mirrored by an analogous development for fermionic models. In this work, we introduce a framework of tensor networks having a fermionic component capable of capturing notions of topological order. At the heart of the formalism are axioms of fermionic matrix product operator injectivity, stable under concatenation. Building upon that, we formulate a Grassmann number tensor network ansatz for the ground state of fermionic twisted quantum double models. A specific focus is put on the paradigmatic example of the fermionic toric code. This work shows that the program of describing topologically ordered systems using tensor networks carries over to fermionic models.

I will discuss two instances of one-dimensional conducting edge channels that can appear on the boundary of three-dimensional topological crystalline insulators, one supported by an experimental observation and the second one being a theoretical prediction. For the first part, I will discuss channels that appear at step edges on the surface of (Pb,Sn)Se. These conducting channels can be understood as arising from a Berry curvature mismatch between Dirac surface states on either side of the step edge. Experimentally, they have been found to be remarkably robust against defects, magnetic fields and elevated temperature. Second, I will introduce the concept of higher-order three-dimensional topological insulators, which have gapped surfaces, but support topologically protected gapless states on their one-dimensional physical edges.

Understanding the robustness of topological phases of matter in the presence of strong interactions, and synthesising novel strongly-correlated topological materials, lie among the most important and difficult challenges of modern theoretical and experimental physics. In this work, we present a complete theoretical analysis of the synthetic Creutz-Hubbard ladder, which is a paradigmatic model that provides a neat playground to address these challenges. We put special attention to the competition of correlated topological phases and orbital quantum magnetism in the regime of strong interactions. These results are furthermore confirmed and extended by extensive numerical simulations. Moreover we propose how to experimentally realize this model in a synthetic ladder, made of two internal states of ultracold fermionic atoms in a one-dimensional optical lattice. Our work paves the way towards quantum simulators of interacting topological insulators with cold atoms. J. Jünemann, A. Piga, S.-J. Ran, M. Lewenstein, M. Rizzi, and A. Bermudez arXiv:1612.02996

Out-of-time ordered (OTO) correlation functions describe scrambling of information in correlated quantum matter. They are of particular interest in incoherent quantum systems lacking well defined quasi-particles. Thus far, it is largely elusive how OTO correlators spread in incoherent systems with diffusive transport governed by a few globally conserved quantities. Here, we study the dynamical response of such a system using high-performance matrix-product-operator techniques. Specifically, we consider the non-integrable, one-dimensional Bose-Hubbard model in the incoherent high-temperature regime. Our system exhibits diffusive dynamics in time-ordered correlators of globally conserved quantities, whereas OTO correlators display a ballistic, light-cone spreading of quantum information. The slowest process in the global thermalization of the system is thus diffusive, yet information spreading is not inhibited by such slow dynamics. We furthermore develop an experimentally feasible protocol to overcome some challenges faced by existing proposals and to probe time-ordered and OTO correlation functions. Our study opens new avenues for both the theoretical and experimental exploration of thermalization and information scrambling dynamics.

The last years have witnessed dramatic progress in experimental control and theoretical modeling of quantum simulations based on ultracold atoms. Major recent developments include synthetic gauge fields for neutral atoms, induced by time-periodic driving of the system, which allow the simulation of topologically nontrivial phases of matter with strong interactions. I will discuss two examples: We present a systematic study of spectral functions of a time-periodically driven Falicov-Kimball Hamiltonian. In the high-frequency limit, this system can be effectively described as a Harper-Hofstadter-Falicov-Kimball model. Using real-space Floquet dynamical mean-field theory (DMFT), we take into account interaction effects and contributions from higher Floquet bands in a non-perturbative way. Our calculations show a high degree of similarity between the interacting driven system and its effective static counterpart with respect to spectral properties. We also demonstrate the possibility of using real-space Floquet DMFT to study edge states on a cylinder geometry. We furthermore consider a spinful and time-reversal invariant version of the Hofstadter-Harper problem, which has been realized in ultracold atoms, with an additional staggered potential and spin-orbit coupling. Without interactions, the system exhibits various phases such as topological and normal insulator, metal and semi-metal phases with two or even more Dirac cones. Using real-space dynamical mean-field theory (DMFT), we investigate the stability of the Quantum Spin Hall state in the presence of strong interactions. To test the bulk-boundary correspondence between edge mode parity and bulk Chern index of the interacting system, we calculate an effective topological Hamiltonian based on the local self-energy of DMFT.

Using a combination of numerically exact and renormalization-group techniques we study the nonequilibrium transport of electrons in an one-dimensional interacting system subject to a quasiperiodic potential. For this purpose we calculate the growth of the mean-square displacement as well as the melting of domain walls. While the system is nonintegrable for all studied parameters, there is no on finite region default of parameters for which we observe diffusive transport. In particular, our model shows a rich dynamical behavior crossing over from superdiffusion to subdiffusion. We discuss the implications of our results for the general problem of many-body localization, with a particular emphasis on the rare region Griffiths picture of subdiffusion.

The Mott transition is a key phenomenon in strongly correlated electron systems. Despite its relevance for a wide range of materials, fundamental aspects of this transition are still unresolved. Of particular interest is the role of the lattice degrees of freedom in the Mott transition. In this talk, we will present results of the thermal expansion coefficient as a function of Helium-gas pressure around the Mott transition of the organic charge-transfer salt $\kappa$-(BEDT-TTF)$_2$Cu[N(CN)$_2$]Cl. The salient result of our study is the observation of a strong, highly non-linear lattice response upon approaching the second-order critical endpoint of the transition. This apparent breakdown of Hooke’s law of elasticity reflects an intimate, non-perturbative coupling of the critical electronic degrees of freedom to the crystal lattice. Our results are fully consistent with mean-field criticality, predicted theoretically for electrons coupled to a compressible lattice with finite shear modulus [2]. [1] E. Gati et al., Science Advances 2: e1601646 (2016) [2] M. Zacharias et al., Phys. Rev. Lett. 109, 176401 (2012) Work has been done in collaboration with E. Gati, M. Garst, R.S. Manna, U. Tutsch, B. Wolf, L. Bartosch, T. Sasaki, H. Schubert, and J.A. Schlueter

We analyze the competition of magnetism and superconductivity in the two-dimensional Hubbard model with a moderate interaction strength, including the possibility of incommensurate spiral magnetic order. Using an unbiased renormalization group approach, we compute magnetic and superconducting order parameters in the ground state. In addition to previously established regions of Neel order coexisting with d-wave superconductivity, the calculations reveal further coexistence regions where superconductivity is accompanied by incommensurate magnetic order [1]. We show that a Fermi surface reconstruction due to spiral antiferromagnetic order may explain the rapid change in the Hall number in a strong magnetic field as recently observed near optimal doping in cuprate superconductors. The single-particle spectral function in the spiral state exhibits hole pockets which look like Fermi arcs due to a strong momentum dependence of the spectral weight [2]. [1] H. Yamase, A. Eberlein, and W. Metzner, Phys. Rev. Lett. 116, 096402 (2016). [2] A. Eberlein, W. Metzner, S. Sachdev, and H. Yamase, Phys. Rev. Lett. 117, 187001 (2016).

I describe the hybrid momentum-real-space DMRG method and discuss applications to multichain and two-dimensional Hubbard models at and away from half-filling and with and without frustration.

The discovery of high-temperature superconductivity in the cuprates has stimulated intense study of the Hubbard and t-J models on a square lattice. However, the accurate simulation of these models is one of the major challenges in computational physics. In this talk I report on recent progress in simulating the Hubbard model at a particularly challenging point in the phase diagram, $U/t=8$, and doping $\delta=1/8$, at which an extremely close competition between a uniform d-wave superconducting state and different types of stripe states is found. Here I mostly focus on results obtained with infinite projected-entangled pair states (iPEPS) - a variational tensor network approach where the accuracy can be systematically controlled by the so-called bond-dimension D. Systematic extrapolations to the exact, infinite D limit show that the fully-filled stripe ordered state is the lowest energy state. Consistent results are obtained with density matrix embedding theory, the density matrix renormalization group, and constrained-path auxiliary field quantum Monte Carlo, demonstrating the power of current state-of-the-art numerical methods to solve challenging open problems.

Dynamical mean field theory (DMFT) has been a big step forward for our understanding of electronic correlations. A major part of the electronic correlations, the local ones, are included. On the other hand, DMFT neglects non-local correlations that are at the origin of many physical phenomena such as (quantum) criticality, high-T superconductivity, weak localization and other vertex corrections to transport in nanoscopic systems. To address these topics the scientific frontier moved to cluster and diagrammatic extensions of DMFT such as the dynamical vertex approximation [1,2]. I will present an introduction to the diagramtic extensions of DMFT and discuss selected applications: the calculation of quantum critical exponents rendering Kohn lines in the bandstructure [3], the fate of the Mott-Hubbard metal-insulator tranistion in two dimensions [4], and the application to realisitc materials calcualtions [5]. [1] A. Toschi, A. A. Katanin, and K. Held, Phys. Rev. B 75, 045118 (2007). [2] G. Rohringer et al., in preparation. [3] T. Schäfer et al., arXiv:1605.06355. [4] T. Schäfer et al., Phys. Rev. B 91, 125109 (2015). [5] A. Galler et al., Phys. Rev. B 95, 115107 (2016).

I will present a numerical scheme to address correlated quantum impurities out of equilibrium down to the Kondo scale. This Auxiliary Master Equation Approach [1,2,3] is also suited to deal with transport across correlated interfaces within nonequilibrium Dynamical Mean Field Theory [5]. The method consists in mapping the original impurity problem onto an auxiliary open quantum system including bath orbitals as well as a coupling to a Markovian environment. The mapping becomes exponentially exact upon increasing the number of bath orbitals. The intervening auxiliary orbitals allow for a treatment of non-Markovian dynamics at the impurity. The time dependence of the auxiliary system is controlled by a Lindblad master equation whose parameters are determined via an optimization scheme. Green's functions are evaluated via (non-hermitian) Lanczos exact diagonalisation [2] or by matrix-product states (MPS) [3]. In particular, the MPS implementation produces highly accurate spectral functions for the Anderson impurity model in the Kondo regime. The approach can be also used in equilibrium, where we obtain a remarkably close agreement to numerical renormalization group. I will present results for electric and thermal transport across an Anderson impurity [2,3,4] and across correlated interfaces [5]. An implementation within Floquet theory for periodic driving [6] will be discussed as well. [1] E. Arrigoni et al., Phys. Rev. Lett. 110, 086403 (2013) [2] A. Dorda et al., Phys. Rev. B 89 165105 (2014) [3] A. Dorda et al., Phys. Rev. B 92, 125145 (2015) [4] A. Dorda et al., Phys. Rev. B 94, 245125 (2016) [5] I. Titvinidze et al., Phys. Rev. B 92, 245125 (2015) [6] M. Sorantin et al., in preparation.

A multi-orbital impurity solver for dynamical mean field theory (DMFT) is presented, which employs a tensor network similar to Matrix Product States. It yields high spectral resolution at all frequencies. The solver works directly on the real-time / real-frequency axis and yields high spectral resolution at all frequencies. We use a large number (O(100)) of bath sites, and therefore achieve an accurate representation of the bath. The solver can treat full rotationally invariant interactions with reasonable numerical effort. We first show the efficiency and accuracy of the method by a benchmark for the three-orbital testbed material SrVO3, where we observe multiplet structures in the high-energy spectrum which are almost impossible to resolve by other multi-orbital methods. Finally we will present new results for five-orbital models.

We investigate the transport properties of strongly correlated materials in the framework of nonequilibrium dynamical mean field theory, where we use the hierarchical quantum master equation approach to solve the respective impurity problem [1,2]. The approach employs a hybridization expansion which can be converged if the temperature of the environment is not too low [3]. It is time-local and can, therefore, be used to study the long-lived dynamics inherent to this problem, including the nonequilibrium steady states. Different truncation levels allow for a systematic analysis of the relevant physical processes. Our results elucidate, in particular, the role of inelastic processes for the transport properties of materials that can be described by the Hubbard model. [1] Jin et al., JCP 128, 234703 (2008); [2] Härtle et al., PRB 88, 235426 (2013); [3] Härtle et al., PRB 92, 085430 (2015).

We review some recent advancements in tensor network algorithms and their application to the study of correlated matter. We present novel approaches to study abelian and non-abelian lattice gauge theories, open many-body quantum systems and systems with long-range interactions or periodic boundary conditions. These novel approaches allowed us to obtain results on a variety of phenomena hardly accessible before, such as the Kibble-Zurek mechanism in Wigner crystals, the out-of-equilibrium dynamics of the Schwinger model and the phase diagram of the disordered Bose-Hubbard model.

Understanding and controlling the relaxation process of optically excited charge carriers in solids with strong correlations is of great interest in the quest for new strategies to exploit solar energy. Usually, optically excited electrons in a solid thermalize rapidly on a femtosecond to picosecond timescale due to interactions with other electrons and phonons. New mechanisms to slow down thermalization would thus be of great significance for efficient light energy conversion, e.g. in photovoltaic devices. Ultrafast optical pump probe experiments in the manganite Pr$_0.65$Ca$_0.35$MnO$_3$, a photovoltaic, thermoelectric and electro-catalytic material with strong polaronic correlations, reveal an ultra-slow recombination dynamics on a nanosecond-time scale [1]. The nature of long living excitations is further elucidated by photovoltaic measurements, showing the presence of photo-diffusion of excited electron-hole polaron pairs [1,2]. Theoretical considerations suggest that the excited charge carriers are trapped in a hot polaron state. The dependence of the lifetime on charge order implies that strong correlation between the excited polaron and the octahedral dynamics of its environment appears to be substantial for stabilizing the hot polaron [3]. Furthermore, modification of the interfacial atomic and electronic structure of the manganite-titanite junctions gives insights into the processes underlying the transfer of a small polaron between materials with different correlations [4]. [1] Evolution of hot polaron states with a nanosecond lifetime in a manganite, D. Raiser, S. Mildner, B. Ifland, M. Sotoudeh, P. Blöchl, S. Techert, C. Jooss, Advanced Energy Materials, 2017, 1602174, DOI: 10.1002/aenm.201602174. [2] Polaron absorption for photovoltaic energy conversion in a manganite-titanate pn-heterojunction, G. Saucke, J. Norpoth, D. Su, Y. Zhu and Ch. Jooss, Phys. Rev. B 85, 165315 (2012). [3] Contribution of Jahn-Teller and charge transfer excitations to the photovoltaic effect of manganite/titanite heterojunctions, B. Ifland, J. Hoffmann, B. Kressdorf, V. Roddatis, M. Seibt and Ch. Jooss, New Journal of Physics, accepted for publication. [4] Current–voltage characteristics of manganite–titanite perovskite junctions, B. Ifland, P. Peretzki, B. Kressdorf, Ph. Saring, A. Kelling, M. Seibt and Ch. Jooss, Beilstein Journal of Nanotechnology, 2015, 6, 1467–1484

Weak perturbations can drive an interacting many-particle system far from its initial equilibrium state if one is able to pump into degrees of freedom approximately protected by conservation laws. This concept has for example been used to realize Bose-Einstein condensates of photons, magnons, and excitons. Integrable quantum system like the one-dimensional Heisenberg model are characterized by an infinite set of conservation laws. Here we develop a theory of weakly driven integrable systems and show that pumping can induce huge spin or heat currents even in the presence of integrability breaking perturbations, since it activates local and quasi-local approximate conserved quantities. The resulting steady state is approximately, though efficiently, described by a generalized Gibbs ensemble, which depends sensitively on the structure but not on the overall amplitude of perturbations or on the initial state. We suggest to realize novel heat or spin pumps using spin-chain materials driven by THz radiation.

Condensed matter is found in a variety of phases, the vast majority of which are characterized in terms of symmetry breaking. However, the last few decades have yielded a plethora of theoretically proposed quantum phases of matter which fall outside this paradigm. Recent focus lies on the search for concrete realizations of quantum spin liquids. These are notoriously difficult to identify experimentally because of the lack of local order parameters. In my talk, I will discuss universal properties found in dynamical response functions that are useful to characterize these exotic states of matter. First, we show that the anyonic statistics of fractionalized excitations display characteristic signatures in threshold spectroscopic measurements. The low energy onset of associated correlation functions near the threshold show universal behavior depending on the statistics of the anyons. This explains some recent theoretical results in spin systems and also provides a route towards detecting statistics in experiments such as neutron scattering and tunneling spectroscopy [1]. Second, we introduce a matrix-product state based method to efficiently obtain dynamical response functions for two-dimensional microscopic Hamiltonians, which we apply to different phases of the Kitaev-Heisenberg model. We find significant broad high energy features beyond spin-wave theory even in the ordered phases proximate to spin liquids. This includes the phase with zig-zag order of the type observed in α-RuCl3, where we find high energy features like those seen in inelastic neutron scattering experiments. [1] S. C. Morampudi, A. M. Turner, F. Pollmann, and F. Wilczek, arXiv:1608.05700. [2] M. Gohlke, R. Verresen, R. Moessner, and and F. Pollmann, arXiv:1701.04678.

Strongly correlated quantum particles with half-integer spin are of growing interest in many fields, including condensed matter, dense plasmas and ultracold atoms. From a theory point of view these systems are very challenging. Also, ab initio quantum simulations such as DMRG are essentially limited to the 1D case. Here, I will present an example of recent breakthroughs we could achieve using a Nonequilibrium Green functions approach [1] that has recently allowed us to simulate the nonequilibrium transport in 2D and 3D fully including strong correlation effects. We achieve, for the first time, excellent agreement with ultracold atom experiments [2]. Our results are close to DMRG results where they are available but, in many cases, allow for much longer simulations [3]. I will close by discussing prospects of using NEGF for transport and optics of solids as well as solids in contact with a plasma [4]. [1] Michael Bonitz, "Quantum Kinetic Theory", 2nd edition, Springer 2016. [2] Niclas Schlünzen, Sebastian Hermanns, Michael Bonitz, and Claudio Verdozzi, Phys. Rev. B 93, 035107 (2016). [3] Niclas Schlünzen, Jan-Philip Joost, Fabian Heidrich-Meisner, and Michael Bonitz, Phys. Rev. B (2017) [4] Karsten Balzer, Niclas Schlünzen, Jan-Philip Joost, and Michael Bonitz, Phys. Rev. B 94, 245118(2016).

Femtosecond laser technology has opened the possibility to probe and control the dynamics of complex condensed matter phases on microscopic timescales. In this talk, I will focus on various proposals to manipulate complex states with spin and orbital order, using the electric field of the laser. This can be done both in the transient regime, where one can use short field transients to switch between different polarizations of a composite orbital order, and for periodic driving, where the laser-driven system effectively evolves with a Floquet-Hamiltonian with light-induced spin and orbital exchange interactions.

The venerable phenomena of Anderson localization, along with the much more recent many-body localization, both depend crucially on the presence of disorder. The latter enters either in the form of quenched disorder in the parameters of the Hamiltonian, or through a special choice of a disordered initial state. Here, we present a model with localization arising in a very simple, completely translationally invariant quantum model, with only local interactions between spins and fermions. By identifying an extensive set of conserved quantities, we show that the system generates purely dynamically its own disorder, which gives rise to localization of fermionic degrees of freedom. Our work gives an answer to a decades old question whether quenched disorder is a necessary condition for localization. It also offers new insights into the physics of many-body localization, lattice gauge theories, and quantum disentangled liquids.

We investigate the time evolution of the Kondo resonance in response to a quench by applying the time-dependent numerical renormalization group (TDNRG) approach to the Anderson impurity model in the strong correlation limit [1]. For this purpose, we derive within TDNRG a numerically tractable expression for the retarded two-time nonequilibrium Green function $G(t+t',t)$, and its associated time-dependent spectral function, $A(\omega,t)$, for times $t$ both before and after the quench. Quenches from both mixed valence and Kondo correlated initial states to Kondo correlated final states are considered. For both cases, we find that the Kondo resonance in the zero temperature spectral function only fully develops at very long times $t\gtrsim 1/T_{\rm K}$, where $T_{\rm K}$ is the Kondo temperature of the final state. In contrast, the final state satellite peaks develop on a fast time scale $1/\Gamma$ during the time interval $-1/\Gamma \lesssim t \lesssim +1/\Gamma$, where $\Gamma$ is the hybridization strength. Initial and final state spectral functions are recovered in the limits $t\rightarrow -\infty$ and $t\rightarrow +\infty$, respectively. Our formulation of two-time nonequilibrium Green functions within TDNRG provides a first step towards using this method as an impurity solver within nonequilibrium dynamical mean field theory. Finally, we show how to improve the calculation of spectral functions in the long time limit within a new multiple quench TDNRG approach with potential application to precise steady state transport calculations for quantum dots [2]. [1] H. T. M. Nghiem and T. A. Costi, arXiv:1701.07558 [2]F. B. Anders, Phys. Rev. Lett. {\bf 101}, 66804 (2008)

The fate of the fermionic quasiparticles near a quantum phase transition (QPT) in certain heavy-fermion compounds where the Hertz-Moriya-Millis scenario does not apply has been subject of intense debate for many years. It is generally believed that this Kondo destruction is driven by the critical fluctuations near the QPT. Here we show that the heavy-fermion quasiparticles can be destroyed by the RKKY interaction even without critical fluctuations [1]. This is due to a hitherto unrecognized interference of Kondo screening and the RKKY interaction beyond the Doniach scenario: In a Kondo lattice, the spin exchange coupling between a local spin and the conduction electrons acquires nonlocal contributions due to conduction electron scattering from surrounding local spins and subsequent RKKY interaction. We develop a novel type of renormalization group theory for this RKKY-modified Kondo vertex [1]. The Kondo temperature, $T_K(y)$, is suppressed in a universal way, controlled by the dimensionless RKKY coupling parameter y. Complete spin screening ceases to exist beyond a critical RKKY strength $y_c$ even in the absence of magnetic ordering. At this breakdown point, $T_K(y)$ remains nonzero and is not defined for larger RKKY couplings, $y>y_c$. These results agree quantitatively with STM spectroscopy experiments on continuously tunable two-impurity Kondo systems [2] and on two-site Kondo systems on a metallic surface [3]. We discuss in detail most recent time-resolved THz reflectometry experiments on the heavy-fermion compound $CeCu_{6-x}Au_x$ at the quantum critical concentration x=0.1 [4]. In these experiments, the spectral weight as well as the energy scale $T_{K}^*$ for the formation of the heavy-fermion quasiparticles can be extracted from the intensity and the delay time, respectively, of a Kondo-induced, THz reflex. THz artifacts, e.g., reflexes from the optical components, are carefully excluded. Both experiment and theory support a quantum critical scenario in $CeCu_{6-x}Au_x$ where the heavy-fermion quasiparticles disintegrate near the QPT in that their spectral weight collapses, but their resonance width (the lattice Kondo temperature $T_K^*$) remains finite. This is consistent with $\omega/T$ scaling as an indicator for critical Kondo destruction. [1] A. Nejati, K. Ballmann, and J. Kroha, Phys. Rev. Lett. 118, 117204 (2017). [2] J. Bork, Y.-H. Zhang, L. Diekhöhner L. Borda, P. Simon, J. Kroha, P. Wahl, and K. Kern, Nature Physics 7, 901 (2011). [3] N. Neel, R. Berndt, J. Kröger, T. O. Wehling, A. I. Lichtenstein, and M. I. Katsnelson, Phys. Rev. Lett. 107, 106804 (2011): A. Nejati and J. Kroha, arXiv:1612.06620 (2016). [4] Ch. Wetli, J. Kroha, K. Kliemt, C. Krellner, O. Stockert, H. von Löhneysen, and M. Fiebig, arXiv:1703.04443.

We show that the two impurity Anderson model exhibit an additional quantum critical point at infinitely many specific distances between both impurities for an inversion symmetric 1D dispersion. Unlike the quantum critical point previously established by Jones and Varma, it is robust against particle-hole or parity symmetry breaking. The quantum critical point separates a spin doublet from a spin singlet ground state and is, therefore, protected by symmetry. A finite single particle tunneling t or an applied uniform gate voltages will drive the system across the quantum critical point. The discriminative magnetic properties of the different phases cause a jump in the spectral functions at low temperature which might be useful for future spintronics devices. A local parity conservation will prevent the spin-spin correlation function to decay to its equilibrium value after spin-manipulations.

This talk will address the question on the ground state of real spin-ice systems. Spin-ice are magnetic systems, Dy$_2$Ti$_2$O$_7$ to name one example, that are charaterised by big magnetic moments sitting on a pyrochlore lattice. At first instance, the interaction between these moments leads to magnetic frustration and the expectation of a extensively degenerate ice-like ground state. Theoretical work and recent experimental evidence put this naive expectation into question. In this talk I will discuss experimental work and numerical simulations on two different spin-ice systems, Dy$_2$Ti$_2$O$_7$ and Ho$_2$Ti$_2$O$_7$, that aim at elucidating the true ground state of spin-ice materials.

Spin ices, frustrated magnetic materials analogous to common water ice, have emerged over the past fifteen years as exemplars of high frustration in three dimensions. By analyzing existing experimental data and carefully remeasuring the thermodynamic quantity $\chi T$ we find that in this material, small effective spin-spin exchange interactions compete with the magnetostatic dipolar interaction responsible for the main spin ice phenomenology. This causes an unexpected 'refrustration' of the long-range order that would be expected from the incompletely self-screened dipolar interaction and which positions the material at the boundary between two competing classical long-range ordered ground states, very close to where theory suggests that a continuous transition described by a noncompact CP$^1$ theory. Furthermore, experimentally we find a interaction induced peak in $\chi T$, which constitutes a magnetic analogue of the Joule temperature in classical gases.

Exotic spin-multipolar ordering in large spin transition metal insulators has so far eluded unambiguous experimental observation. A less studied, but perhaps more feasible fingerprint of multipole character emerges in the excitation spectrum in the form of quadrupolar transitions. Such multipolar excitations are desirable as they can be manipulated with the use of light or electric field and can be captured by means of conventional experimental techniques. Here we study single crystals of multiferroic Sr2CoGe2O7, and show that due to its nearly isotropic nature a purely quadrupolar bimagnon mode appears in the electron spin resonance (ESR) spectrum. This non-magnetic spin-excitation couples to the electric field of the light and becomes observable for a specific experimental configuration, in full agreement with a theoretical analysis of the selection rules.

The recent discovery that strongly spin-orbital coupled magnets such as alpha-RuCl3, may display a broad excitation continuum inconsistent with conventional magnons has lead to the proposal of having a possible realization of a Kitaev spin liquid with a coherent continuum of majorana excitations. In this talk we discuss the underlying interactions in alpha-RuCl3 and present a more general scenario to describe the observed continuum that is consistent with ab initio calculations and available experimental observations.

We study the real-time dynamics of a single spin in an external magnetic field, coupled antiferromagnetically to an extended system of conduction electrons which is initiated by a sudden switch of the field direction. The problem is treated numerically by means of tight-binding spin dynamics (TB-SD) assuming the spin as a classical observable and by time-dependent density-matrix renormalization group (t-DMRG). Effects of conduction-electron correlations, of quantum spin fluctuations, and energy dissipation are shown to result in various anomalous effects, such as ill-defined Gilbert damping, incomplete spin relaxation due to time-scale separation, quantum nutation, and precessional motion with enhanced effective Larmor frequency due to a geometrical torque.

Recent developments in diverse areas - ranging from cold atomic gases to light driven semiconductors to microcavity arrays - move systems into the focus which are located on the interface of quantum optics, many-body physics and statistical mechanics. They share in common that coherent and driven?dissipative quantum dynamics occur on an equal footing, creating genuine non-equilibrium scenarios without immediate counterpart in equilibrium condensed matter physics. We study such systems in two dimensions on the basis of a duality transformation mapping the problem into a non-linear noisy electrodynamics, where the charges represent vortices. In the absence of vortices, the problem is equivalent to the Kardar-Parisi-Zhang equation. We show that the paradigmatic quasi-long range order of equilibrium systems at low temperature must be absent asymptotically. More precisely, the non-equilibrium drive generates two independent scales, leading to distinct but subalgebraic behavior of the asymptotic correlation functions. Although the usual Kosterlitz-Thouless phase transition does thus not exist out of equilibrium, a new phase transition into a vortex turbulent state is found, which occurs as a function of increasing non-equilibrium strength.

The real-time broadening of density profiles starting from non-equilibrium states is at the center of transport in condensed-matter systems and dynamics in ultracold atomic gases. Initial profiles close to equilibrium are expected to evolve according to linear response, e.g., as given by the current correlator evaluated exactly at equilibrium. Significantly off equilibrium, linear response is expected to break down and even a description in terms of canonical ensembles is questionable. We unveil that single pure states with density profiles of maximum local amplitude yield a broadening in perfect agreement with linear response, if the structure of these states involves randomness in terms of decoherent off-diagonal density-matrix elements. While these states allow for spin diffusion in the XXZ spin-1/2 chain at large exchange anisotropies, coherences yield entirely different behavior [1]. In contrast, charge diffusion in the strongly interacting Hubbard chain turns out to be stable against varying such details of the initial conditions [2]. [1] R. Steinigeweg, F. Jin, D. Schmidtke, H. De Raedt, K. Michielsen, J. Gemmer, Phys. Rev. B 95, 035155 (2017). [2] R. Steinigeweg, F. Jin, H. De Raedt, K. Michielsen, J. Gemmer, arXiv:1702.00421 (2017).

Time-resolved pump-probe experiments recently attracted great interest, since they allow to detecting hidden states and they provide new information on the underlying dynamics in solids in real time. With the observation of a Higgs mode in superconductors it is now possible to investigate the superconducting order parameter directly. Recently, we have established a theory for superconductors in non-equilibrium, for example in a pump-probe experiment. Using the Density-Matrix-Theory (DMT) we have developed an approach to calculate the response of conventional and unconventional superconductors in a time-resolved experiment. In particular, DMT method is not restricted to small timescales; in particular it provides a microscopic description of the quench, and also allows also the incorporation of phonons. Furthermore, we employ DMT to time-resolved Raman scattering experiments and make predictions for 2-band superconductors. Very recently, we have focused on the theory for order parameter amplitude (‘Higgs’) oscillations which are the realization of the Higgs mode in superconductors [1]. New predictions are made for the Leggett mode in 2-band superconductors. Finally, we address the question of induced superconductivity in non-equilibrium. Many of our predictions have been recently confirmed experimentally. References: [1] H. Krull et al., Nat. Comm. 7, 11921 (2016).

We present results for the dynamical thermal conductivity of the Kitaev-Heisenberg model on ladders and the Kitaev model on honeycomb lattices. In the pure Kitaev limit, and in contrast to other integrable spin systems, the ladder represents a perfect heat insulator. This is a fingerprint of fractionalization into mobile Majorana matter and a static Z2 gauge field. We find a full suppression of the Drude weight and a pseudogap in the conductivity. With Heisenberg exchange, we find a crossover from a heat insulator to conductor, due to recombination of fractionalized spins into triplons. For the honeycomb lattice, we show that very similar behavior occurs in 2D. Our results rest on several approaches comprising a mean-field theory, complete summation over all gauge sectors, exact diagonalization, and quantum typicality calculations.

We measure and compute the transport properties of two-dimensional ultracold Fermi gases during transverse demagnetization in a magnetic field gradient. Using a phase-coherent spin-echo sequence, we are able to distinguish bare spin diffusion from the Leggett-Rice effect, in which demagnetization is slowed by the precession of spin current around the local magnetization. When the two-dimensional scattering length is tuned to be comparable to the inverse Fermi wave vector, we find that the bare transverse spin diffusivity reaches a minimum of order $\hbar/m$. The rate of demagnetization is also reflected in the growth rate of the s-wave contact, which quantifies how scale invariance is broken by near-resonant interactions. Our observations support the conjecture that in systems with strong scattering, the local relaxation rate is bounded from above by $kT/\hbar$, in analogy with what is found in materials with $T$-linear resistivity. [1] C. Luciuk, S. Smale, F. Boettcher, H. Sharum, B.A. Olsen, S. Trotzky, T. Enss, and J. H. Thywissen, Phys. Rev. Lett. (2017), arXiv:1612.00815.

We investigate the spinless Anderson-Holstein model routinely employed to describe the basic physics of phonon-assisted tunneling in molecular devices. Our focus in on small to intermediate electron-phonon coupling; we complement a recent strong coupling study [Phys. Rev. B 87, 075319 (2013)]. The entire crossover from the antiadiabatic regime to the adiabatic one is considered. Our analysis using the essentially analytical functional renormalization group approach backed-up by numerical renormalization group calculations goes beyond lowest order perturbation theory in the electron-phonon coupling. In particular, we provide an analytic expression for the effective tunneling coupling at particle-hole symmetry valid for all ratios of the bare tunnel coupling and the phonon frequency. It contains the exponential polaronic as well as the power-law renormalization; the latter can be traced back to x-ray edge-like physics. In the antiadibatic and the adiabatic limit it agrees with the known expressions obtained by mapping to an effective interacting resonant level model and lowest order perturbation theory, respectively. In addition, we discuss spectral and linear transport properties of the model.

The properties of collective phases occuring in strongly correlated materials are characterized by their correlations and the occuring orders. The controlled switching of these properties requires the understanding of the evolution of the correlations and the order after an excitation of the system. This excitation can be the application of an electric field or the switching of other system parameters. A lot of work has been done on the propagation of correlations in isolated systems. Here we will focus on the evolution in systems under the influence of an environment as the phononic coupling represents in materials or light field in cold atomic samples. The states considered are topologically non-trivial states or pairing states.

Tensor network states and specifically matrix-product states have proven to be a powerful tool for simulating ground states of strongly correlated spin and fermionic models. In this contribution, we focus on tensor network states techniques that can be used for the treatment of high-dimensional optimization tasks in strongly correlated quantum many-body systems with long range interactions. We will present our recent developments on fermionic orbital optimization and tree-tensor network states and discuss properties of various strongly correlated systems in light of the entanglement which gives insight into the fundamental nature of the correlations in their ground states. Examples will be shown for extended periodic systems, transition metal complexes and graphene nanoribbons.

In this talk I will briefly present three recent advances in tensor network states and techniques for 2d quantum lattice systems. Namely, (i) the classification of SU(2) spin liquids with PEPS and their characterization via the entanglement spectrum in cylinders, (ii) a new algorithm for computing steady states of 2d dissipative systems, and (iii) the holographic encoding of universal properties in the spectra of corner transfer matrices and corner tensors in numerical simulations with infinite PEPS.

I will give an overview of our recent work on many-body localization in infinite chains with binary disorder. I will discuss the phase diagram as well as possible realizations of such systems using cold atomic gases. In a second part, I will discuss Anderson and many-body localization in ladder-like systems.

There has recently been a flurry of negative sign free fermionic models that exhibit exotic phases and phase transitions. After reviewing these advances, I will place the emphasis on a model of Dirac fermions in 2+1 dimensions with dynamically generated, anti-commuting SO(3) N\'eel and Z2 Kekul\'e mass terms. The phase diagram is obtained from finite-size scaling and includes a direct and continuous transition between N\'eel and Kekul\'e phases. The fermions remain gapped across the transition, and our data support an emergent SO(4) symmetry unifying the two order parameters. This is only one of many negative sign free models with dynamically generated competing mass terms that allow to investigate phase transitions beyond the Ginzburg-Landau-Wilson paradigm.

In the presence of an elastic coupling, the strong fluctuations of critical modes close to a second-order phase transition might induce an elastic phase transition of the crystal lattice. In this case, the long-range shear forces of the crystal fundamentally influences the critical properties [1]. One can distinguish isostructural transitions, where the crystal symmetry remains unchanged, and symmetry-breaking elastic phase transitions. The former is relevant for the universality of the Mott endpoint at finite temperature [2], which is corroborated by recent experiments of expansivity in an organic conductor [3]. We discuss symmetry-breaking elastic quantum phase transitions in general, for which the critical thermodynamics of phonons violate Debye’s law [4]. Finally, we argue that elasticity is relevant for nematic quantum criticality [5], that is discussed to be relevant to the cuprates, ruthenates and pnictides. [1] M. Zacharias, A. Rosch, and M. Garst Critical elasticity at zero and finite temperature, Eur. Phys. J. Special Topics 224, 1021 (2015) [2] M. Zacharias, L. Bartosch, and M. Garst, Mott metal-insulator transition on compressible lattices, Phys. Rev. Lett. 109, 176401 (2012) [3] E. Gati, M. Garst, R. S. Manna, U. Tutsch, B. Wolf, L. Bartosch, H. Schubert, T. Sasaki, J. A. Schlueter, and M. Lang, Breakdown of Hooke’s law of elasticity at the Mott critical endpoint in an organic conductor, Science Advances 2, e1601646 (2016). [4] M. Zacharias, I. Paul, and M. Garst, Quantum critical elasticity, Phys. Rev. Lett. 115, 025703 (2015) [5] I. Paul and M. Garst, Lattice effects on nematic quantum criticality in metals, arXiv:1610:06168

We present quantum Monte Carlo results for the charge-density-wave transition of Luttinger and Fermi liquids coupled to quantum phonons. The power of a new directed-loop algorithm for retarded interactions is demonstrated for the one-dimensional Holstein model. In two dimensions, the critical temperature and Ising universality as well as the nature of the disordered phase are investigated using the continuous-time interaction expansion method.

We consider a chain of atoms that are bound together by a harmonic force. Spin-1/2 electrons that move between neighboring chain sites (Hückel model) induce a lattice dimerization at half band filling (Peierls effect). We supplement the Hückel model with a local Hubbard interaction and a long-range Ohno potential, and calculate the average bond-length, dimerization, and optical phonon frequencies for finite straight and zig-zag chains using the density-matrix renormalization group (DMRG) method. We check our numerical approach against analytic results for the Hückel model. The Hubbard interaction mildly affects the average bond length but substantially enhances the dimerization and increases the optical phonon frequencies whereas, for moderate Coulomb parameters, the long-range Ohno interaction plays no role.

Recent years have witnessed rapid progress in the use of integrability in characterizing the out-of-equilibrium dynamics of low-dimensional systems such as interacting atomic gases and quantum spin chains. This talk will provide an introduction to these developments.

Dynamical quantum phase transitions (DQPTs) have emerged as a nonequilibrium analogue to conventional phase transitions with physical quantities becoming nonanalytic at critical times. I will summarize the recent developments including the first experimental observations of DQPTs in systems of ultracold gases in optical lattices as well as trapped ions. While the formal analogies of DQPTs to equilibrium phase transitions are straightforward, a major challenge is to connect to fundamental concepts such as scaling and universality. In this talk I will show that for DQPTs in Ising models exact renormalization group transformations in complex parameter space can be formulated. As a result of this construction, the DQPTs turn out to be critical points associated with unstable fixed points of equilibrium Ising models implying scaling and universality in this far-from equilibrium regime.

I will discuss the transport of information in generic one-dimensional quantum systems using various measures. As a local probe, one can use out-of-time order correlation functions, which quantify the growth of the commutator of local operators in time. They exhibit a light-cone structure in chaotic (weakly disordered or Floquet) systems, which becomes a logarithmic light cone in strongly disordered many-body localized (MBL) systems and a power law light-cone at intermediate disorder, where particles are presumably transported subdiffusively. Both cases illustrate a slow, subballistic information propagation, which is reflected in a sublinear power-law growth of the entanglement entropy after a quench from a product state in a subdiffusive system and a logarithmic growth in the MBL case. The propagation of information is a generic property of the time evolution operator and therefore also visible in the operator space entanglement entropy of the evolution operator.

We study the time evolution in the Tomonaga--Luttinger model (TLM) and the transverse-field Ising chain (TFIC) subject to quantum quenches of finite duration, ie, a continuous change in the interaction strength or transverse magnetic field respectively. We analyse several observables including two-point correlation functions, which show a characteristic bending and delay of the light cone due to the finite quench duration. For example, we extract the universal behaviour of the Green functions in the TLM and provide analytic, non-perturbative results for the delay. As another example, for quenches between the phases in the TFIC we show that the Loschmidt echo exhibits characteristic non-analyticities due to a dynamical phase transition, which show clear signatures of the finite quench duration.

We present two matrix-product-state methods for investigating quantum transport in one-dimensional correlated electron-phonon systems. The time-evolving block decimation method with local basis optimization (TEBD-LBO) [1] allows us to simulate the nonequilibrium dynamics of many-particle systems with strongly fluctuating bosonic degrees of freedom. Thus we can study nonlinear transport properties [2] and dissipation effects [1,3]. We also show that the dynamical DMRG combined with linear response theory [4] enables the calculation of the linear conductance in Luttinger liquids using a proper scaling of system length, zero-frequency current-current correlation functions, and broadening. This approach works for lattice models of Luttinger liquids including impurities, phonons or contacts to metallic leads. [1] C. Brockt, F. Dorfner, L. Vidmar, F. Heidrich-Meisner, and E. Jeckelmann, Phys. Rev. B 92, 241106(R) (2015). [2] M. Einhellinger, A. Cojuhovschi, and E. Jeckelmann, Phys. Rev. B 85, 235141 (2012). [3] Christoph Brockt and Eric Jeckelmann, Phys. Rev. B 95, 064309 (2017). [4] D. Bohr, P. Schmitteckert, and P. W\"{o}lfle, Europhys. Lett. 73, 246 (2006)."

I will discuss a special class of Mott insulators, where spin-orbit coupling dictates a nonmagnetic $J=0$ ground state, and the magnetic response is given by gapped singlet-triplet excitations. Exchange interactions as well as crystalline electric fields may close the spin gap, resulting in a Bose condensation of spin-orbit excitons. In addition to usual magnons, a Higgs amplitude mode, most prominent near quantum critical point, is expected. Upon electron doping, ferromagnetic correlations and triplet superconductivity may emerge. These predictions [1,2] will be discussed in the context of recent neutron and Raman light scattering experiments [3,4] in ruthenium oxides. [1] G. Khaliullin, Phys.Rev.Lett. {\bf 111}, 197201 (2013). [2] J. Chaloupka and G. Khaliullin, Phys.Rev.Lett. {\bf 116}, 017203 (2016). [3] A. Jain {\it et al.}, Nature Phys. 2017 (in press). [4] M. Souliou {\it et al.}, unpublished.

In Mott insulators, unquenched orbital degrees of freedom often frustrate the magnetic interactions and lead to a plethora of interesting phases with unusual spin patterns or non-magnetic states without long-range order. I will review from this perspective the theoretical concepts and experimental data on the late transition metal compounds, mostly focusing on iridates. In the second part, I will present our recent theoretical study of interplay of spin and orbital degrees in double-perovskite compounds with spin one-half ions occupying the frustrated fcc sublattice, such as molybdenum and osmium oxides. I will argue that this interplay might lead to a rich variety of the phases that include non-collinear ordered patterns with or without net moment, and, most remarkably, non-magnetic disordered spin-orbit dimer state.

We study strongly-correlated $t_{2g}$ systems with strong spin-orbit coupling. The case of one hole, i.e. five electrons, per site has attracted considerable attention in the context of iridates: The hole is thought to be well modelled by a spin-like $j=1/2$ degree of freedom and the versatile material class has been proposed to host topologically nontrivial states as well as an analogue to cuprate superconductors. We well here, however, concentrate on two related but different scenarios. The first is the case of one \emph{electron}, which has in contrast addition to the $j=1/2$ pseudospin also an orbital degree of freedom. We will discuss (combined) spin and orbital excitation spectra expected for such cases. The second scenario to be discussed is given by two holes, i.e., a $d^4$ configuration. While the single-site ground state is here a (boring) singlet, triplet excitations do not have very high energies, so that magnetic couplings can lead to exciton condensation and magnetic order. We will present a honeycomb lattice with a Kitaev-Heisenberg-like bond geometry. The difference to the well-studied $d^4$ case is that the spin-length can here fluctuate, and we will discuss the impact of this difference as well as the magnetic excitations expected for the various phases.

The Heisenberg model for S=1/2 describes the interacting spins of electrons localized on lattice sites due to strong repulsion. It is the simplest strong-coupling model in condensed matter physics with wide-spread applications. Its relevance has been boosted further by the discovery of curate high-temperature superconductors. In leading order, their undoped parent compounds realize the Heisenberg model on square-lattices. Much is known about the model, but mostly at small wave vectors, i.e., for long-range processes, where the physics is governed by spin waves (magnons), the Goldstone bosons of the long-range ordered antiferromagnetic phase. Much less, however, is known for short-range processes, i.e., at large wave vectors. Yet these processes are decisive for understanding high-temperature superconductivity. Recent reports suggest that one has to resort to qualitatively different fractional excitations, spinons [1]. By contrast, we present a comprehensive picture in terms of dressed magnons with strong mutual attraction on short length scales [2]. The resulting spectral signatures agree strikingly with experimental data [3]. [1] Dalla Piazza et al., Nature Physics 11, 62 (2015). [2] M. Powalski, G.S. Uhrig, and K.P. Schmidt, PRL 115, 207202 (2015). [3] M. Powalski, K.P. Schmidt, and G.S. Uhrig, arXiv:1701.04730 (2017).

Correlation effects, in particular intra- and interorbital electron-electron interactions, are very substantial in 3d transition-metal compounds such as the copper oxides, but relativistic spin-orbit coupling (SOC) is weak. In 5d transition-metal compounds such as iridates, the interesting situation arises that the SOC and Coulomb interactions meet on the same energy scale. The electronic structure of iridates thus depends on a strong competition between the electronic hopping amplitudes, local energy-level splittings, electron-electron interaction strengths, and the SOC of the Ir 5d electrons. The interplay of these ingredients offers the potential to stabilize relatively well-understood states such as a 2D Heisenberg-like antiferromagnet in Sr$_2$IrO$_4$, but in principle also far more exotic ones, such a topological Kitaev quantum spin liquid, in (hyper)honeycomb iridates [1-3]. I will discuss the microscopic electronic structures of these iridates, their proximity to idealized Heisenberg and Kitaev models and our contributions to establsihing the physical factors that appear to have preempted the realization of quantum spin liquid phases so far. [1] Jackeli & Khaliullin, PRL 102, 017205 (2009) [2] Nussinov & Van den Brink, RMP 87, 1 (2015), arXiv:1303.5922 [3] Gretarsson et al., PRL 110, 076402 (2013), Lupascu et al., PRL 112, 147201 (2014), Katukuri et al., NJP 16, 013056 (2014), Katukuri et al., PRX 4, 021051 (2014), Kim et al., Nature Comm. 5, 4453 (2014), Bogdanov et al., Nature Comm. 6, 7306 (2015), Nishimoto et al., Nature Comm. 7, 10273 (2016), Plotnikova et al., PRL 116, 106401 (2016)

Motivated by recent STM experiments on chains of Co adatoms deposited on Cu2N that have revealed a series of ground state level crossings as a function of magnetic field [1], and by their possible connection to Majorana edge states [2], I will discuss the origin of level crossings in the transverse field Ising model perturbed by an additional spin-spin interaction parallel or perpendicular to the magnetic field. I will show that, in a chain of N spins, an additional spin-spin interaction induces N level crossings in the ground state however small it might be, provided it has the same sign as the main interaction [3]. The proof relies on a mapping on Kitaev's 1D model of a p-wave superconductor [4], for which it can be shown that similar level crossings occur provided the pairing amplitude is smaller than the hopping integral due to the oscillating character of the Majorana edge states [3-6]. [1] R. Toskovic, R. van den Berg, A. Spinelli, I. S. Eliens, B. van den Toorn, B. Bryant, J.-S. Caux, and A. F. Otte, Nat. Phys. 12, 656 (2016). [2] F. Mila, Nat. Phys. 12, 633 (2016). [3] G. Vionnet, B. Kumar, F. Mila, arXiv:1701.08057. [4] A. Y. Kitaev. Phys.-Usp. 44 131 (2001). [5] H.-C. Kao, Phys. Rev. B 90, 245435 (2014). [6] Suraj S. Hegde and Smitha Vishveshwara, Phys. Rev. B 94, 115166 (2016).

We address the problem of computing the thermodynamic properties of the repulsive one-dimensional two-component Fermi gas and the two-component Bose gas with contact interaction. We derive an exact system of only two non-linear integral equations for the thermodynamics of the homogeneous model. This system allows for an easy and extremely accurate calculation of thermodynamic properties circumventing the difficulties associated with the truncation of the thermodynamic Bethe ansatz system of equations. We present extensive results for the densities, polarization, magnetic susceptibility, specific heat, interaction energy, Tan contact and local correlation function of opposite spins. Our results show that at low and intermediate temperatures the experimentally accessible contact is a non-monotonic function of the coupling strength. As a function of the temperature the contact presents a pronounced local minimum in the Tonks-Girardeau regime which signals an abrupt change of the momentum distribution in a small interval of temperature. The density profiles of the system in the presence of a harmonic trapping potential are computed using the exact solution of the homogeneous model coupled with the local density approximation. At finite temperature the density profile presents a double shell structure only when the polarization in the center of the trap is above a critical value.

Andreas Weichselbaum ^1, Sylvain Capponi ^2, Andreas Läuchli ^3, Alexei Tsvelik ^4, and Philippe Lecheminant ^5 ^1 Ludwig Maximilians University, Munich, Germany ^2 CNRS Toulouse, Université Paul Sabatier, France ^3 University of Innsbruck, Austria ^4 Brookhaven National Laboratory, Upton, NY, USA ^5 Université de Cergy Pontoise, France The density matrix renormalization group (DMRG) is applied to $SU(N)$ symmetric Heisenberg chains and ladders while fully exploiting the underlying $SU(N)$ symmetry. Since these models can be motivated from symmetric

The exactly solvable Tomonaga-Luttinger model describes two flavors of interacting electrons with linear dispersion in one dimension, but some of its properties are characteristic for a wider class of one-dimensional systems according to the Luttinger liquid paradigm [1]. The exact solution for linear dispersion is based on bosonization, which represents fermionic particle-hole excitations in terms of canonical bosons and maps the Tomonaga-Luttinger Hamiltonian onto a free bosonic theory. We use the framework of constructive finite-size bosonization [2] to derive explicit bosonic representations of general bilinear fermion operators including arbitrary dispersion terms. As an application, Luttinger `droplets' with position-dependent parameters are investigated. [1] F. D. M. Haldane, J. Phys. C: Solid State Phys. 14, 2585 (1981). [2] J. von Delft and H. Schoeller, Ann. Phys. 7, 225 (1998).

The antiferromagnetic spin-one chain is considerably one of the most fundamental quantum many-body systems. We perform a comparative study of its dynamical spin structure factor at finite temperatures, using exact diagonalization, quantum Monte Carlo simulations, and in particular a recently developed finite-temperature matrix-product-state method working in frequency space. Firstly, open chain ends yield localized edge states whose low-frequency spectral signatures persist at finite temperatures. Moreover, we observe the thermal activation of a distinct low-energy continuum contribution to the spin spectral function with an enhanced spectral weight at low momenta and its upper threshold. This emerging thermal spectral feature of the antiferromagnetic spin-one chain is argued to result from intraband magnon scattering due to the thermal population of the single-magnon branch, which features a large bandwidth-to-gap ratio in the present system. [1] J. Becker, T. Köhler, A.C. Tiegel, S.R. Manmana, S. Wessel, A. Honecker, Phys. Rev. B 96, 060403(R), 060403(R) (2017)

In recent years a growing number of vertex models or (super-)spin chains arising in the description of disorder problems or intersecting loops have been found to possess a continuous spectrum of crtitical exponents. In the lattice model this is accompanied by strong finite size corrections in the spectrum of low energy excitations. For the corresponding effective field theory this implies the presence of primary fields with weights taking continuous values within some interval. We address the question of how to characterize such a spectrum and to identify the corresponding conformal field theory in these systems.

In recent years we have combined van Vleck's `method of moments' with methods for the exact calculation of short-range temperature-dependent correlation functions in order to explain the response of Heisenberg-type spin chains to ESR experiments. In this talk I review our results and some of the general problems connected with the description of the micro-wave absorption by exchange interacting spin systems. Our insight is then used to interpret recent experimental data on the quasi-1d compound Cu (py)_2 Br_2.

Unusual magnetocaloric properties are a hallmark of magnetic spin systems with competing interactions. In this presentation I am going to introduce molecular magnetic systems with strong frustration. I will demonstrate links to extended quantum magnets. The magnetocaloric properties can be evaluated by means of the finite-temperature Lanczos method which produces quasi-exact results. The method will be explained shortly and then applied to several investigated systems.

In this talk, I will discuss a particularly simple way to fractionalization, namely the emergence of quasiparticles of charge e/2 in spin-orbit coupled quantum wires with strong interactions. This physics may already have an experimental realization. It also has promising applications: coupling a wire hosting quasiparticles of charge e/2 to a standard superconductor leads to an 8$\pi$-Josephson effect, and to topological zero energy states bound to interfaces.

The existence of a non-magnetic spin-liquid ground state of the spin-1/2 kagome Heisenberg antiferromagnet (KHAF) is well established. Meanwhile, also for the spin-1 KHAF evidence for the absence of magnetic long-range order (LRO) was found. On the other hand, recently it has been reported that magnetic LRO can be established by (i) increasing the spin quantum number to s>1 [1,2], (ii) by including an easy-plane anisotropy for s=1 [3,4], as well as (iii) by an interlayer coupling in a layered kagome system [5]. Another route to magnetic LRO is given by including further neighbor couplings [6,7]. We briefly review the results of [1-7] and present new results for the ground-state phase diagram for the J1-J2 KHAF (where J1 is the nearest-neighbor coupling and J2 is the 2nd neighbor coupling) for spin quantum numbers s=1/2 and s=1 using the Coupled-Cluster Method (CCM) in high orders of approximation and Lanczos exact diagonalization of finite lattices of up to N=36 sites. Starting from the pure KHAF (i.e., at J2=0) we find that a finite strength of the 2nd neighbor coupling J2 is necessary to drive the system from the spin-liquid state to a ground state with magnetic LRO either of $q=0$ symmetry (for antiferromagnetic J2) or of $\sqrt{3} \times\sqrt{3}$ symmetry (for ferromagnetic J2), where the CCM allows to determine the critical values of J2. We also study thermodynamic properties by using the high-temperature expansion (HTE) up to 13th order [8]. The tendency to establish ground-state LRO of $q=0$ or $\sqrt{3} \times \sqrt{3}$ symmetry can already be seen in the static spin structure factor S(q) at temperatures T of the order of J1. Increasing the strength of J2, in S(q) maxima at those magnetic wave vectors Q arise that correspond to the $q=0$ or $\sqrt{3} \times \sqrt{3}$ symmetry. By using Pade approximants of the HTE series we can compute the uniform susceptibility $\chi(T)$ and the magnetic specific heat $c(T)$ down to temperatures of T$\sim$0.6J1, where the 2nd neighbor coupling J2 has already a noticeable effect on the temperature profile of $\chi(T)$ and $c(T)$. By using a scheme interpolating between the low-energy and high-energy degrees of freedom [9] we also calculate the specific heat below T=0.6J1. While for the pure KHAF an extraordinary large value of $c(T)$ at low temperatures is present, the 2nd neighbor coupling J2 may lead to a more conventional temperature profile of $c(T)$. [1] O. Goetze, D.J.J. Farnell, R.F. Bishop, P.H.Y. Li, and J. Richter, Phys. Rev. B 84, 224428 (2011). [2] J. Oitmaa and R. R. P. Singh, Phys. Rev. B 93, 014424 (2016). [3] A. L. Chernyshev and M. E. Zhitomirsky, Phys. Rev. Lett. 113, 237202 (2014). [4] O. Goetze and J. Richter, Phys. Rev. B 91, 104402 (2015). [5] O. Goetze and J. Richter, Europhys. Lett. (EPL) 114, 67004 (2016). [6] Y. Iqbal, D. Poilblanc, and F. Becca, Phys. Rev. B 91, 020402 (2015). [6] Y. Iqbal, D. Poilblanc, and F. Becca, Phys. Rev. B 91, 020402 (2015). [7] H.J. Liao, Z.Y. Xie, J. Chen, Z.Y. Liu, H.D. Xie, R.Z. Huang, B. Normand, T. Xiang, arXiv:1610.04727. [8] A. Lohmann, H.-J. Schmidt, and J. Richter, Phys. Rev. B 89, 014415 (2014). [9] H.J. Schmidt, A. Hauser, A. Lohmann, and J. Richter, arXiv:1702:00487, Phys. Rev. E accepted.

In this talk I discuss the topological Kondo effect realized in Majorana box devices. With normal leads, it represents a stable isotropic multi-channel Kondo fixed point that can be probed by linear conductance measurements. With superconducting leads, we predict a 6pi periodicity of the Josephson current, corresponding to fractionalized charge transfer.

We study the effect of classical critical fluctuations of the superconducting order parameter on the electronic properties in the normal state of a clean superconductor in three dimensions. Using a functional renormalization group approach to take the non-Gaussian nature of critical fluctuations into account, we show that in the vicinity of the critical temperature $T_c$ the electronic density of states exhibits a fluctuation-induced pseudogap. Moreover, in the BCS regime where the inverse coherence length is much smaller than the Fermi wavevector, classical critical order parameter fluctuations give rise to a non-analytic contribution to the quasi-particle damping of order $ ( T_c^3 / E_F^2 ) \ln ( 80 / Gi )$, where $E_F$ is the Fermi energy and the Ginzburg-Levanyuk number $Gi$ is a dimensionless measure for the width of the critical region. In the BCS regime where $Gi$ is typically in the range between $10^{-14}$ and $10^{-12}$ there is a sizable range of temperatures above $T_c$ where the quasiparticle damping due to critical superconducting fluctuations is larger than the usual $T^2$-quasi-particle damping in three-dimensional Fermi-liquids. On the other hand, in the strong coupling regime where $Gi$ is of order unity we find that the quasiparticle damping due to critical pairing fluctuations is proportional to the temperature. We also use functional renormalization group methods to derive and classify various types of induced interaction processes due to particle-hole fluctuations in Fermi systems close to the superconducting instability.

In my talk I will consider the interplay between superconductivity and formation of bound pairs of fermions in multi-band 2D fermionic systems (BCS-BEC crossover). In two spatial dimensions a bound state develops already at weak coupling, and BCS-BEC crossover can be analyzed already at weak coupling, when calculations are fully under control. We found that the behavior of the compensated metal with one electron and one hole bands is different in several aspects from that in the one-band model. There is again a crossover from BCS-like behavior at EF>>E0 (E0 being the bound state energy formation in a vacuum) to BEC-like behavior at EF<< E0 with Tins > Tc. However, in distinction to the one-band case, the actual Tc, below which long-range superconducting order develops, remains finite and of order Tins even when EF = 0 on both bands. The reason for a finite Tc is that the filled hole band acts as a reservoir of fermions. The pairing reconstructs fermionic dispersion and transforms some spectral weight into the newly created hole band below the original electron band and electron band above the original hole band. A finite density of fermions in these two bands gives rise to a finite Tc even when the bare Fermi level is exactly at the bottom of the electron band and at the top of the hole band. I also analyze the formation of the s+is state in a four-band model across the Lifshitz transition including BCS-BEC crossover effects on the shallow bands. Similar to the BCS case, we find that with hole doping the phase difference between superconducting order parameters of the hole bands change from 0 to π through an intermediate s + is state, breaking time-reversal symmetry (TRS).