Korrelationstage 2019

The recent developments of femtosecond photon sources from the Thz to ultraviolet spectral range have largely enriched the methods to probe condensed matter on ultrafast timescales. Among the possible approaches, time resolved photoemission spectroscopy is acquiring an increasing recognition because of the unique capability of visualizing the temporal evolution of electronic excitations. I review the basic principles of this experimental method and discuss the results that we have obtained in the cuprate family of high temperature superconductors. Relevant examples are the estimate of average electron-phonon coupling and the photoinduced melting of superconducting phase. Both the physics of the non-equilibrium and critical condensate is ruled by fluctuations of the pairing field. These ones are responsible for the softening the superfluid stiffness and the partial filling of the superconducting gap. In the second part of the seminar I introduce the principles of time resolved THz spectroscopy. The THz data trade the lack of wavevector information by a considerable gain in signal to noise ratio. In particular, the high sensitivity of to superconducting correlations enables an inspection of the critical regime and reveals that fluctuating condensate obeys a scaling law casting information on the universality class.

In recent years the study of out-of-equilibrium systems allowed to unveil the transformation between the entanglement entropy and the thermodynamic entropy. Here we investigate the dynamics of the entanglement entropy after a quench from piecewise homogeneous initial conditions in interacting integrable models. By combining the quasiparticle picture for the entanglement spreading with the Generalized Hydrodynamic approach (GHD) we derive an exact formula for the dynamics of the entanglement entropy. We also consider the entanglement entropy between two semi-innite chains. Remarkably, we show that the entanglement production rate depends only on the physics at the interface between the two halves of the system. Furthermore, we highlight several intriguing effects, due to the presence of interactions. Most remarkably, we show that the entanglement production rate is different from the rate of exchange of thermodynamic entropy between the two systems. This is different for quenches in free fermions, where they coincide.

The fascinating Sachdev-Ye-Kitaev (SYK) model describing a large number of randomly interacting Majorana fermions represents an ultimate example of the AdS/CFT correspondence in 1+1 space-time dimensions. As pointed out by Kitaev, both the SYK model and its gravity dual possess an emergent conformal symmetry which, however, is spontaneously broken in the infra-red. As such, the soft (or Goldstone) mode in the spectrum of the model emerges which is known to be described by the so-called 'Schwarzian' action. In my talk, after a general exposition to the SYK model, I will concentrate on its generalisation to the granular quantum matter defined by SYK quantum dots coupled via random one-body hopping. Within the framework of Schwarzian field theory, I will show how a zero temperature quantum phase transition between an insulating phase at weak and a metallic phase at strong hopping can be identified. The critical hopping strength scales inversely with the number of degrees of freedom on the dots. The increase of temperature out of either phase induces a crossover into a regime of strange metallic behavior.

There is a concentrated effort in understanding chaotic dynamics in a wide range of many-body classical and quantum systems. This includes work on the quantum bound on chaos and scrambling, the theory of structural glasses, but also the physics of SYK models. A central role in this effort is played by the “out-of-time-ordered commutators” which are used to diagnose many-body chaos in terms of the butterfly effect. We establish this phenomenology in a class of frustrated magnets, which allow chaos to survive until low (zero) temperature due to competing inter- actions resulting in a largely degenerate ground state and un-quenched entropy. In this way classical frustration and spin liquids provide a clean platform to study many-body chaotic dynamics, make quantitative relations between transport quantities (such as diffusion) and measures of many-body chaos, and gain insight into the relevance of OTOC in classical systems and the semi-classical limit of quantum chaos.

One intriguing phenomenon in nature is the rich interplay between coexisting phases or competing orders in various complex systems. To gain insights to possible fundamental nature of such interplay, we recently studied the effects of external driving in a Bose-Einstein condensate inside a high-finesse optical cavity. This system hosts a competition between a homogeneous condensate phase and a self-organized density wave phase, leading to a superradiant phase transition as the intensity of transverse pump beam is increased. Motivated by the challenges of light-induced superconductivity, we demonstrate dynamical control of this superradiant transition via periodic driving of the pump laser. We show that the dominant density wave order of the superradiant state can be suppressed leading to the restoration of coherence in the BEC. Accompanying experimental results confirm our prediction of light-induced coherence in the atom-cavity system. Our work then establishes a minimal model for a hypothesized mechanism for light-induced superconductivity. Furthermore, we show that additional, non-equilibrium density wave orders, which do not exist in equilibrium, can be stabilized dynamically, and finally, that for strong driving chaotic dynamics emerges.

Iron-based superconductors display a variety of magnetic phases originating in the competition between electronic, orbital, and spin degrees of freedom. Inelastic neutron scattering (INS) has recently confirmed the existence of an antiferromagnetic $\uparrow\uparrow\downarrow\downarrow$-pattern along the legs of quasi-one dimensional iron-based materials, as predicted for the orbital-selective Mott phase (OSMP) of the multi-orbital systems. This unusual spin-block state was observed in ladder BaFe$_2$Se$_3$ and in two-dimensional systems with iron vacancies, such as Rb$_{0.89}$Fe$_{1.58}$Se$_2$ and K$_{0.8}$Fe$_{1.6}$Se$_2$. Moreover, the powder INS spectrum reveled an unexpected structure, containing both low-energy acoustic and high-energy optical modes. We will show that the former represents the spin-wave-like dynamics of the block ferromagnetic islands, while the latter is attributed to a novel type of local on-site spin excitations controlled by the Hund coupling. Furthermore, we will show that electron-doping of the OSMP induces a whole class of novel block-states with a variety of periodicities beyond the previously reported pattern. We also derived the effective Hamiltonian of the OSMP, the generalized Kondo-Heisenberg model, which describes all magnetic phases and allow for an intuitive understanding of the origin of the block magnetism.

We consider the longitudinal and transverse dynamic structure factors in impurity doped spin-1/2 chains. The impurities lead to effectively isolated finite chain segments with a discrete spectrum and characteristic correlations, which have a distinct effect on the dynamic structure factors. We present very accurate results for the low energy spectral weight obtained by numerical Density Matrix Renormalization Group techniques and identify the character of dominant excitations for a large range of doping concentrations, anisotropies, and fields. In comparison with finite-size bosonization we find surprisingly good agreement with the numerical results. This has direct relevance for recent experiments on spin chains and ultracold gases and shows that, contrary to expectations, bosonization works especially well for short chains and in the vicinity of divergences. Finally, we discuss characteristic signatures in the dynamic structure factors when going from dilute defects to random disorder.

The concept of quantum typicality presents a novel route to computing finite temperature properties of quantum many-body systems. We demonstrate, how to use the Lanczos method in conjunction with quantum typicality to extract thermodynamic quantities at arbitrary temperatures without a full diagonalization of the Hamiltonian. This technique is applied to compute the thermodynamics of the frustrated spin compound $SrCu_2(BO_3)_2$, where recently a pressure-induced quantum phase transition has been observed. Our results on system sizes up to 40 spins are compared to Quantum Monte Carlo and iPEPS simulations.

We introduce a special kind of tree tensor networks that has geometry of a comb. We develop an efficient variational optimization of the wave-function in a comb geometry and compare its complexity with one of the density matrix renormalization group (DMRG) algorithm. We apply the algorithm to study the low-energy properties of Heisenberg model on a comb lattice. We show that spin-1/2 edge states of the Haldane spin-1 teeth form a critical spin-1/2 chain along a backbone. When the backbone coupling is sufficiently strong the first site of each tooth form a Haldane chain along a backbone, so the spin-1/2 edge states are localized at the second site of each tooth, however the system remains critical due to effective antiferromagnetic interaction between these edge states. Two regimes are connected by a smooth crossover. Even more interesting are the results of spin-1/2 comb. In this case one can view the comb tensor network as a chain of complicated zero-dimensional objects, each of which is critical in the thermodynamic limit. Magnon excitations are delocalized over the whole lattice and energy gap decays faster than 1/N that one can naturally expect for 1+1D conformal field theory.

In quantum magnets spins form well-defined lattices and serve as model systems to study many-body quantum phases such as interacting quantum-dimer qubits, spin Luttinger-liquids, Bose glasses, or magnon Bose-Einstein condensates. Neutron, muon and photon sources are unique tools for high-precision studies of such phases, and of their correlations and excitations in as well as out of equilibrium. An overview of current frontiers in the field will be presented with special focus on recent developments in computational physics and exciting new opportunities that free electron lasers like SwissFEL and European XFEL will offer to study the time-dependence and out-of-equilibrium quantum mechanics of such systems.

Margherita Boselli$^{1}$, Claribel Dominguez$^{1}$, Jennifer Fowlie$^{1}$, Marta Gibert$^{2}$, Celine Lichtensteiger$^{1}$, Hugo Meley$^{1}$, Gernot Scheerer$^{1}$, Adrien Waelchli$^{1}$, Bernat Mundet$^{3}$, Duncan Alexander$^{3}$, Stefano Gariglio$^{1}$, and Jean-Marc Triscone$^{1}$ $^{1}$DQMP, University of Geneva, 24 Quai Ernest-Ansermet, 1211 Geneva 4, Switzerland $^{2}$Physik-Institut, University of Zurich, Winterthurerstrasse 190, 8057 Zurich, Switzerland $^{3}$EPFL - IPHYS – LSME Station 3, CH-1015 Lausanne, Switzerland In this talk, I will discuss several interfacial couplings that occur in oxide heterostructures. Polar discontinuities can lead to 2-dimensional conduction between insulating materials – I will briefly discuss the case of the LaAlO$_3$/SrTiO$_3$ system [1,2]; Structural and electronic coupling at oxide interfaces can also lead to interesting phenomena that we investigated in perovskite nickelates - well-known for their metal to insulator transition (MIT) and unique antiferromagnetic ground state [3-5] – there, I will show that NdNiO$_3$/SmNiO$_3$ superlattices display, depending on the thickness of the individual layers, a single or double MIT - a behavior that allows the role of interfacial structural and electronic coupling in heterostructures to be studied. Finally I will present results on vanadate-based heterostructures where we aimed at designing an artificial ferroelectric material [6,7]. In this system, the interface sharpness seems to be controlled by the coupling of distortions and periodicity of the structure. [1] A. Ohtomo, H. Y. Hwang, Nature 427, 423 (2004). [2] N. Reyren, S. Thiel, A. D. Caviglia, L. Fitting Kourkoutis, G. Hammerl, C. Richter, C. W. Schneider, T. Kopp, A.-S. Ruetschi, D. Jaccard, M. Gabay, D. A. Muller, J.-M. Triscone and J. Mannhart, Science 317, 1196 (2007). [3] M.L. Medarde, Journal of Physics Condensed Matter 9, 1679 (1997). [4] G. Catalan, Phase Transitions 81, 729 (2008). [5] S. Catalano, M. Gibert, J. Fowlie, J. Iniguez, J.-M. Triscone, J. Kreisel ,Reports on Progress in Physics 81, 046501 (2018). [6] See, for instance, J. M. Rondinelli and C. J. Fennie, Adv. Mater. 24, 1961 (2012). [7] H. Meley, Karandeep, L. Oberson, J. de Bruijckere, D. T. L. Alexander, J.-M. Triscone, Ph. Ghosez, S. Gariglio, APL Materials 6, 046102 (2018).

We study the quantum effects of spin-fermion coupling in systems where localized spins and itinerant electrons coexist. In general, this coupling leads to corrections in the excitation spectrum of both subsystem and affects, e.g., the electronic scattering rate or the spin susceptibility. In particular, it is interesting to analyze the mutual influence when the individual subsystems possess special quantum degrees of freedom. We illustrate this at two complimentary examples. We determine the damping of spin-waves in an antiferromagnet due to interaction with Dirac electrons as relevant for $YbMnBi_2$. Furthermore, we demonstrate the emergence of clear non-Fermi-liquid behavior in a 3D metal coupled to 1D critical spin chains, a situation realized in $Yb_2Pt_2Pb$.

The spin-orbit Mott insulator Sr${}_2$IrO${}_4$ has raised tremendous interest recently due to striking similarities to high-Tc superconducting copper oxides both in the pure and in electron-doped compounds. Here, we study the evolution of the spectral function of this 5d transition metal system as a function of doping by means of a combined ab-initio electronic structure and many-body quantum cluster approach. Thereby, important ingredients like spin-orbit coupling and distortions of the oxygen octahedra as well as Hubbard interactions and non-local charge fluctuations are taken into account. The spectral function of pure Sr${}_2$IrO${}4$ is analyzed both in its high-temperature paramagnetic and its low-temperature antiferromagnetic phase and the importance of non-local fluctuations is discussed. The spectra compare well with angle-resolved photoemission measurements and allow us to study emerging changes under electron- and hole-doping. For electron-doped Sr${}_2$IrO${}_4$, special emphasis is placed on pseudogap features of the spectral function, which are found to be in good agreement with experiment. Furthermore, we discuss an intriguing k-dependence in the composition of the spin-orbit entangled $j_{\mathrm{eff}}=1/2$ states.

Gapless Dirac fermions appear in various condensed-matter scenarios as for example in graphene and related materials, but also in the dual description of the deconfined quantum critical point between Neel and valence bond solid orders in frustrated quantum magnets. The precise determination of the critical behavior of Dirac fermions defines a prime benchmark for complementary theoretical approaches and moreover will allow us to test conjectures based on duality arguments. In my talk, I present a comprehensive analysis of the Gross-Neveu universality classes based on the recently achieved four-loop renormalization group calculations and compare to Monte Carlo and the conformal bootstrap. Further, I will show a three-loop study of deconfined criticality from the dual QED3-Gross-Neveu model and discuss the implications of our estimates for the critical exponents for nontrivial scaling relations which follow from the emergent SO(5) symmetry implied by the duality conjecture.

Following the remarkable discovery of correlated insulators and superconductivity in magic angle twisted bilayer graphene (TBG), a great deal of attention has been lavished on various ``moire materials". We focus on the variety of moire systems where the conduction and valence bands are separated from each other by energy gaps. This is the case when the TBG is further aligned with a hexagonal Boron Nitride substrate (TBG/hBN), but also in different sets of experiments, such as trilayer graphene aligned with hBN, as well as twisted double bilayer graphene systems (i.e. bilayer graphene twisted relative to another bilayer graphene to a magic angle). We further restrict our analysis to the strong interaction limit i.e. when the Coulomb interaction is much bigger than the bandwidth. We show the emergence of a ferromagnetic ground state at quarter, half and three quarter filling of these nearly flat bands. When the band has a non-zero Chern number, the ferromagnetism is accompanied by a quantized anomalous Hall effect. Our results are based on analytical arguments, as well as exact diagonalization and DMRG results which quantitatively show the stability of the ferromagnetic ground state. They provide further theoretical understanding to the observation of ferromagnetism in TBG/hBN[1], TLG/hBN[2] and twisted double bilayer[3], as well as the observation of quantized anomalous Hall effect in some of these systems[2]. [1] Emergent ferromagnetism near three-quarters filling in twisted bilayer graphene, Sharpe et al arXiv:1901.03520 [2] Tunable Correlated Chern Insulator and Ferromagnetism in Trilayer Graphene/Boron Nitride Moire Superlattice, Chen et al arXiv:1905.06535 [3] Spin-polarized Correlated Insulator and Superconductor in Twisted Double Bilayer Graphene, Liu et al arXiv: 1903.08130

Metallic phases which cannot be described in the usual Fermi-liquid framework have been observed in a variety of strongly correlated electron systems, such as cuprates, pnictides and heavy-fermion materials. A widely discussed scenario for such non-Fermi liquid behavior is the presence of a quantum critical point in quasi two dimensional metals, where the strong interaction between electrons and gapless order-parameter fluctuations destroys the electronic quasiparticle coherence. Here we revisit the problem of two-dimensional metals at the onset of incommensurate 2kF charge density wave order. Previous works argued that this transition is potentially first order due to strong fluctuations. Building upon a controlled, perturbative renormalization group approach developed by Dalidovich and Lee [1], which treats electrons and order parameter fluctuations on equal footing, we show that a dynamical nesting of the Fermi surface renders the transition continuous. We discuss properties of this new non-Fermi liquid fixed point and highlight experimental signatures.

Certain U(1) spin liquids with gapless neutral fermions are expected to have the mind-boggling property that their optical conductivity vanishes as a power law of frequency. Thus, they are insulators to DC electric fields but without a "hard" optical gap, allowing them to absorb light at low frequencies. Additionally, they can also develop Landau levels in a magnetic field. In this work, we show that they can also have cyclotron resonance peaks in their optical spectrum analogous to metals, even though they are charge insulators. Interestingly, we have found that in contrast to metals, the principal Kohn harmonic of the cyclotron resonance is missing. The cyclotron resonance could therefore serve as a beautiful smoking gun test for the existence of these states which have been proposed in 2D organic materials and SmB6.

Majorana zero modes are a promising platform for topologically protected quantum information processing. Their non-Abelian nature, which is key for performing quantum gates, is most prominently exhibited through braiding. While originally formulated for two-dimensional (2d) systems, it has been shown that braiding can also be realized using one-dimensional (1d) wires by forming an essentially two-dimensional network. Here, we show that in driven systems far from equilibrium, one can do away with the second spatial dimension altogether by instead using quasienergy as the second dimension. To realize this, we use a Floquet topological superconductor which can exhibit Majorana modes at two special eigenvalues of the evolution operator, 0 and pi, and thus can realize four Majorana modes in a single, driven quantum wire. We describe and numerically evaluate a protocol that realizes a topologically protected exchange of two Majorana zero modes in a single wire by adiabatically modulating the Floquet drive and using the pi modes as auxiliary degrees of freedom.

In 1979, Su, Schrieffer, and Heeger (SSH) introduced a simple microscopic model of polyacetylene with a modulation of the electronic hopping as a result of distortions of the carbon bonds. It has since gained a much wider relevance due to its relation to symmetry-protected topological states. While it is known that quantum lattice fluctuations can destroy the Peierls insulating bond-order-wave (BOW) ground state and lead to a gapless Luttinger-liquid (LL) phase, quantitative results for finite phonon frequencies are rare. Using a recently developed directed-loop quantum Monte Carlo method for retarded interactions we calculate the phase diagram of the spinless SSH model at half-filling for the entire range of phonon frequencies. In addition to the known LL and BOW phases, we find an extended charge-density-wave (CDW) phase at high phonon frequencies that has not been found in previous studies. Because of different broken symmetries, BOW and CDW phases are connected by a retardation-driven phase transition. Our results are consistent with the theory of the frustrated XXZ chain, including unconventional power-law exponents at criticality, and with an interpretation in terms of deconfined quantum criticality via proliferation of solitons.

Excitons interacting with charge carriers in van-der-Waals materials represent a new venue to study the many-body physics of strongly interacting Bose-Fermi mixtures. In order to derive an effective low-energy model for such systems we develop an exact diagonalization approach that predicts the bound-state and scattering properties of electrons, excitons, and trions in two-dimensional semiconductors. By solving the quantum mechanical three-body problem of interacting charge carriers we thus obtain binding energies of excitons and trions that are in excellent agreement with quantum Monte Carlo predictions. Importantly, in our approach also excited states are accessible. This allows us to predict exotic excited trion states as well as to calculate the scattering phase shifts of electrons and excitons. From these results we derive an effective low-energy model of exciton-electron scattering that can serve as an input to advanced many-body techniques. As a demonstration we study the recently observed exciton Fermi polarons, and we demonstrate that effective range corrections predicted by our model have a substantial impact on the optical absorption spectrum of charge-doped transition-metal dichalcogenides. Our approach can similarly be applied to study a plethora of many-body phenomena realizable in atomically thin semiconductors ranging from exciton lattices and localization to induced superconductivity.

Particle-hole symmetry gives rise to novel effects and provides stability to exotic quantum states. We study this at the example of the Hubbard model using fermionic quantum gases in optical lattices. We directly observe the particle-hole symmetry by comparison between the equation of states in the density and spin sectors, which was previously not possible in solid state materials. In addition, we utilise the transformation and detect an "imcompressible" magnetization near the preformed pairs phase.

Quantum phase transitions (QPTs) involve transformations between different states of matter that are driven by quantum fluctuations. These fluctuations play a dominant role in the quantum critical region surrounding the transition point, where the dynamics are governed by the universal properties associated with the QPT. The resulting quantum criticality has been explored by probing linear response for systems near thermal equilibrium. While time dependent phenomena associated with classical phase transitions have been studied in various scientific fields, understanding critical real-time dynamics in isolated, non-equilibrium quantum systems is of fundamental importance both for exploring novel approaches to quantum information processing and realizing exotic new phases of matter. Here, we use a Rydberg atom quantum simulator with programmable interactions to study the quantum critical dynamics associated with several distinct QPTs. By studying the growth of spatial correlations while crossing the QPT at variable speeds, we experimentally verify the quantum Kibble-Zurek mechanism (QKZM) for an Ising-type QPT, explore scaling universality, and observe corrections beyond simple QKZM predictions. This approach is subsequently used to investigate novel QPTs associated with chiral clock model providing new insights into exotic systems, and opening the door for precision studies of critical phenomena and applications to quantum optimization

The doped Fermi-Hubbard model, widely believed to capture the essential features of high-temperature superconductivity, hosts a rich phase diagram which remains subject of debate. Quantum simulators with ultracold atoms in optical lattices offer a radically new perspective on this model, and allow for the first time to fully resolve the complex interplay of spin and charge degrees of freedom. We will start by reviewing recent measurements which found indications for short-range hidden string order and for the first time revealed the magnetic dressing cloud of mobile dopants in real space. Then we will focus on the properties of a single hole inside a quantum anti-ferromagnet, which are studied by a microscopic spinon-chargon trial wavefunction valid at strong couplings: This includes the quasiparticle dispersion, the magnetic polaron radius and the quasiparticle weight Z. The latter is highly anisotropic across the Brillouin zone, and features a sharp drop at the magnetic zone boundary, reminiscent of Fermi-arcs observed in the pseudogap phase of cuprates.

Recent pump-probe experiments on underdoped cuprates and similar systems suggest the existence of a transient superconducting state above $T_c$. This poses the question how to reliably identify the emergence of long-range order, in particular superconductivity, out-of-equilibrium. We investigate this point by studying a quantum quench in an extended Hubbard model and by computing various observables, which are used to identify (quasi-)long-range order in equilibrium. Our findings imply that, in contrast to current experimental studies, it does not suffice to study the time evolution of the optical conductivity to identify superconductivity. In turn, we suggest to utilize time-resolved ARPES experiments to probe for the formation of a condensate in the single- and two-particle channel. Reference: Sebastian Paeckel, Benedikt Fauseweh, Alexander Osterkorn, Thomas Köhler, Dirk Manske, and Salvatore R. Manmana, arXiv:1905.08638

We investigate the full quantum evolution of ultracold interacting bosonic atoms confined to a chain geometry and coupled to the field of an optical cavity. Extending the time-dependent matrix product state techniques to capture the global coupling to the cavity mode and the open nature of the cavity, we fully include the light-atom entanglement. We examine the long time behavior of the system beyond the mean-field elimination of the cavity field. We show that in the self-organized phase the steady state consists in a mixture of the mean-field predicted density wave states and coherent states with lower photon number, with a large entanglement between the atomic and photonic degrees of freedom. In the regime of large dissipation strengths we develop a variant of the many-body adiabatic elimination technique and obtain a highly entangled steady state with a fully mixed atomic sector. We observe numerically the crossover from the density wave state towards the fully mixed state.

Whereas both gapped topologically ordered systems exhibiting fractionalization, and gapless topological semimetals without interactions are well understood, many open questions remain when gapless topology is combined with strong interactions. In my talk, I will present two examples for gapless topological states exhibiting fractionalization, namely a fractional Weyl semimetal and semiquantized quantum Hall states in bilayer graphene systems. I will discuss microscopic model for these states, both of which can be understood in terms of composite quasiparticles composed of gapless fermions glued to fractionalized quasiparticles of a gapped subsystem, and detail physical signatures of such gapless fractionalized phases.

One of the major challenges in condensed matter research consist in identifying and describing mechanisms of control over correlated quantum many-body systems using non-equilibrium means. Three of such mechanisms are (i) non-linear phononics, (ii) preparing meta-stable states as well as (iii) Floquet engineering. We will discuss explicitly one example out of each of these: (i) First, we illustrate how the dominant symmetry-allowed non-linear coupling between electrons and dipole active phonons provides an attractive contribution to the electron-electron interaction. The magnitude of this attraction is proportional to the degree of laser-induced phonon population and may cause, e.g., transient superconductivity [1]. (ii) Then we turn to chiral superconductors and identify a two-pulse sequence of combined linear and circular polarized light that can be used to switch the chirality of the superconducting condensate on an ultra-fast timescale, which might be useful for quantum computation [2]. (iii) Finally, we describe Floquet engineering; the idea to steer system properties by periodic drive. We consider a driven one-dimensional interacting model and show that the drive can be used to flexibly control the different phases found [3]. All these studies hinge on describing out-of-equilibrium correlated electronic many-body systems coupled to phonons and/or light; a formidable challenge to our theoretical understanding. To address this I combined, developed and applied a variety of theoretical tools including tensor network based simulations and functional renormalization group approaches, some of which I will present as well. [1] D.M. Kennes, E.Y. Wilner, D.R. Reichman, A.J. Millis, Nature Physics 13, 479-483 (2017). [2] M. Claassen, D.M. Kennes, M. Zingl, M.A. Sentef, A. Rubio, arXiv:1810.06536 (under review in Nature Physics). [3] D.M. Kennes, A. de la Torre, A. Ron, D. Hsieh, A.J. Millis, Phys. Rev. Lett. 120, 127601 (2018).

Topology a mathematical concept became recently a hot topic in condensed matter physics and materials science. One important criteria for the identification of the topological material is in the language of chemistry the inert pair effect of the s-electrons in heavy elements and the symmetry of the crystal structure [1]. Beside of Weyl and Dirac new fermions can be identified compounds via linear and quadratic 3-, 6- and 8- band crossings stabilized by space group symmetries [2]. In magnetic materials the Berry curvature and the classical AHE helps to identify interesting candidates. Magnetic Heusler compounds were already identified as Weyl semimetals such as Co2YZ [3,4], in Mn3Sn [5,6,7] and Co3Sn2S2 [8]. The Anomalous Hall angle helps to identify even materials in which a QAHE should be possible in thin films. Besides this k-space Berry curvature, Heusler compounds with non-collinear magnetic structures also possess real-space topological states in the form of magnetic antiskyrmions, which have not yet been observed in other materials [9]. [1] Bradlyn et al., Nature 547 298, (2017) arXiv:1703.02050 [2] Bradlyn, et al., Science 353, aaf5037A (2016). [3] Kübler and Felser, Europhys. Lett. 114, 47005 (2016) [4] Chang et al., Scientific Reports 6, 38839 (2016) [5] Kübler and Felser, EPL 108 (2014) 67001 (2014) [6] Nayak, et al., Science Advances 2 e1501870 (2016) [7] Nakatsuji, Kiyohara and Higo, Nature 527 212 (2015) [8] Liu, et al. Nature Physics 14, 1125 (2018):1712.06722 [9] Nayak, et al., Nature 548, 561 (2017)

Recent experiments with ultracold quantum gases in artificial magnetic fields have shown the possibility to study the Hall effect in quasi one-dimensional highly tunable ladder systems. In this context we theoretically analyze the properties of the reactive Hall response on ladder models with strongly interacting bosons and fermions. We compare different methods for the computation of the static Hall coefficient and discuss its dependence on the various methods or limits considered. In the cases relevant for recent experiments in synthetic dimensions, we find a surprising universal behavior of the weak field Hall coefficient of single component phases in the case of an SU(M) symmetric interaction. For strong magnetic fields we study the interesting properties of the quantum-Hall effect in various quantum phases on ladder geometries.

I will discuss interaction effects in two-dimensional Fermi systems with quadratic band touching and C3 rotational symmetry, as realized in (simple models of) bilayer graphene. As a consequence of the low rotational symmetry, interactions can induce a splitting of each quadratic band touching point into four Dirac cones. This leads to a stable semimetallic phase at small interaction strength and a quantum critical point at finite coupling, beyond which the system orders at low temperatures. I will demonstrate that the quantum critical point is characterized by emergent Lorentz symmetry and falls into the (2+1)D Gross-Neveu universality class.

Kitaev honeycomb materials are enticing platforms to realize fractionalized Majorana fermions. Among the most promising candidates is $\alpha$-RuCl$_3$, which evidences clear signatures of a Kitaev spin liquid state [1,2]. However, at low temperatures Heisenberg- and anisotropy terms dominate, culminating in a long-range zig-zag antiferromagnetic order. This can be overcome by applying magnetic fields. At H$_c$ = 6.5 T $\alpha$-RuCl$_3$ approaches quantum criticality. Using Raman spectroscopy we directly probe the emergence of Majorana bound states out of a continuum of itinerant Majorana fermions as applied fields exceed H$_c$. Work supported by QUANOMET NL-4 and DFG LE967/16-1. [1] Sandilands, et al., Phys. Rev. Lett. 114, 147201 (2014). [2] Glamazda, et al., Phys. Rev. B 95, 174429 (2017).

Ultracold atoms in optical lattices are powerful experimental platforms to study a variety of phenomena ranging from condensed-matter to statistical physics. Recently, a promising new direction was opened by the successful realization of two paradigmatic topological condensed matter models, i.e. the Hofstadter and the Haldane model. Topological states of matter exhibit unique conductivity properties, which are particularly robust against perturbations. One of the most prominent examples is the integer quantum Hall effect, where a two-dimensional electron gas under extreme conditions exhibits a quantized conductivity. Investigating related phenomena with charge-neutral atoms required the development of novel experimental techniques to mimic the behavior of charged particles in magnetic fields. I will introduce some of the most common methods using Floquet engineering, i.e. periodic driving of the system’s parameters to emulate the properties of a system that is otherwise not available in static settings. These methods led to the successful generation of artificial magnetic fields in optical lattices and direct observations of the associated non-trivial topological properties in the topological condensed matter models mentioned above. The simulation of complete gauge theories requires additional key ingredients that allow for an interaction between matter and gauge fields. One of the main challenges consists in engineering synthetic gauge fields with internal degrees of freedom that interact with the matter fields in a suitable manner that respects the symmetry of the gauge theory. Here, I will present recent results, where we have used a two-component mixture of ultracold bosonic atoms and resonant periodic driving at the value of the inter-species Hubbard interactions. Choosing particular modulation parameters enables the implementation of a $\mathbb{Z}_2$ symmetric model, which we study in an optical double-well potential -- the basic building block of the $\mathbb{Z}_2$ lattice gauge theory.

I will present our recent study of a quantum many-body lattice system of one-dimensional spinless fermions interacting with a dynamical $Z_2$ gauge field. The gauge field mediates long-range attraction between fermions resulting in their confinement into bosonic dimers. At strong coupling we develop an exactly solvable effective theory of such dimers. Our DMRG results for correlation functions provide evidence for a Luttinger liquid phase at a generic fermion density. We discuss the possibility of a Mott phase at the commensurate filling $2/3$. In a finite chain we observe the doubling of the period of Friedel oscillations which paves the way towards experimental detection of confinement in this system.

The phase diagram of the Fermi-Hubbard model and its connection to high-temperature superconductivity have been the subject of a vast amount of theoretical and experimental studies in the past decades. Here, we present recent results motivated by the new perspective quantum gas microscopes provide. Our theoretical approach, the geometric string theory, describes doped holes moving in an AFM environment as meson-like bound states of spinons and chargons. DMRG simulations of the ground state as well as the dynamics of a single hole show convincing evidence for this scenario. We furthermore compare geometric string theory predictions for spin correlation functions as well as string patterns at finite temperature and finite doping to experimental data of a cold atom experiment and find remarkable agreement. For an unbiased comparison of theories and experiment, we apply machine learning to classify experimental data at finite doping into different theoretical categories in order to determine which theory describes the system best on the microscopic level.

Tensor networks methods are able to simulate static and dynamic properties of strongly correlated quantum systems in condensed matter physics and can successfully deal with complex multi-reference problems in quantum chemistry. They provide a variational ansatz-class based on a controlled correlation structure and allow in dynamical simulations to extract rigorous error bars on the computed quantities. Despite their overall success, the simulation of the non-equilibrium dynamics of quantum system is often hindered by the fast build-up of correlations such that only short time scales are accessible; often too short in order to extract experimental quantities of interest. In fermionic systems this limitation can be overcome. We present a tensor network method which does not only updates the corresponding tensor network state but also dynamically adapts the single particle basis of the problem. This allows in moderately interacting settings to exactly account for a majority of the build-up correlations and to extend the simulation time of those systems significantly. We illustrate our scheme on the one-dimensional Fermi-Hubbard model and show that we can extend the simulation time compared to established tensor network methods

Infinite projected entangled pair states (iPEPS), the tensor network ansatz for two-dimensional systems in the thermodynamic limit, already provide excellent results on ground-state quantities using either imaginary-time evolution or variational optimisation. Here, we show (i) the feasibility of real-time evolution in iPEPS to simulate the dynamics of an infinite system after a global quench and (ii) the application of disorder-averaging to obtain translationally invariant systems in the presence of disorder. To illustrate the approach, we study the short-time dynamics of the square lattice Heisenberg model in the presence of a bi-valued disorder field. In addition to these new research results in two dimensions, I will briefly reference a currently work-in-progress review[*] on time evolution methods for matrix-product states in one dimension. This review collects and explains all current state-of-the-art methods and furthermore applies them to four numerical settings of current interest in an attempt to compare and benchmark the methods in real-world settings. [*] S. Paeckel, T. Köhler, A. Swoboda, S. R. Manmana, U. Schollwöck, C. Hubig: Time evolution methods for matrix-product states (in prep.)

For weak and moderate interactions, the functional renormalization group (fRG) has been developed as a powerful tool to deal with the vast hierarchy of energy scales and competing instabilities in interacting fermion systems. Using the dynamical mean-field theory (DMFT) as a ''booster-rocket'', the fRG can be upgraded from a weak-coupling method to a new approach for strongly interacting fermion systems. For instance, non-perturbative features associated with the Mott metal-insulator transition are already captured by the DMFT. We present the first results for the two-dimensional Hubbard model in the strongly interacting regime. After demonstrating that the full frequency dependence of the two-particle vertex needs to be taken into account, we show that an unbiased treatment of competing correlations is now feasible also for strong interactions. We find strong antiferromagnetic correlations from half-filling to 18 percent hole-doping, and a sizable d-wave pairing interaction driven by magnetic correlations at the edge of the antiferromagnetic regime.

The problem of characterizing low-temperature spin dynamics in antiferromagnetic spin chains has so far remained elusive. Here we reinvestigate it by focusing on isotropic antiferromagnetic chains whose low-energy effective field theory is governed by the quantum non-linear sigma model. Employing an exact non-perturbative theoretical approach, we analyze the low-temperature behaviour in the vicinity of non-magnetized states and obtain exact expressions for the spin diffusion constant and the NMR relaxation rate, which we compare with previous theoretical results in the literature. Surprisingly, in $SU(2)$-invariant spin chains in the vicinity of half-filling we find a crossover from the semi-classical regime to a strongly interacting quantum regime characterized by zero spin Drude weight and diverging spin conductivity, indicating super-diffusive spin dynamics. The dynamical exponent of spin fluctuations is argued to belong to the Kardar-Parisi-Zhang universality class. Furthermore, by employing numerical tDMRG simulations, we find robust evidence that the anomalous spin transport persists also at high temperatures, irrespectively of the spectral gap and integrability of the model.

I will start with a summary of the charge carrier relaxation after the photo-excitation in Mott insulators. First I will describe relevant relaxation channels deep in the Mott phase and close to the metal-insulator transition within the Hubbard model. The relevance of this description will be exemplified by the relaxation dynamics of the photo-emission spectra in 1T-TaS2 [1]. The comparison of the experimental and theoretical spectra will reveal the role of chemical doped charge carriers as an efficient heat bath leading to a non-trivial occupation dynamics. In the second part, I will compare the dynamics after the photo-excitation in Mott and charge-transfer insulators (CTIs). The later is described within the three-band Emery model and a non-equilibrium extension of GW+EDMFT [2]. In contrast to Mott insulators, a strong renormalization of the charge-transfer gap and a substantial broadening of bands is present in CTIs [3]. The comparison with different experimental pump-probe techniques, like time-resolved ARPES and optical conductivity, shows qualitative agreement and exemplify that dynamical correlations are essential for a proper description of the photo-doped state. I will provide an outlook on how to extend these tools to an ab-initio description of strongly correlated materials out of equilibrium. [1] M. Ligges, I. Avigo, DG, H. Strand, L. Stojchevska, M. Kalläne, P. Zhou, K. Rossnagel, M. Eckstein, P. Werner, and U. Bovensiepen. Phys. Rev. Lett. 120, 166401 (2018). [2] DG, L. Boehnke, M. Eckstein, P. Werner, arxiv:1808.02264 (2018) [3] DG, L. Boehnke, H. U. R. Strand, M. Eckstein, P. Werner, Phys. Rev. Lett. 118, 246402 (2018)

Topology is quickly becoming a cornerstone in our understanding of electronic systems. Like their electronic counterparts, bosonic systems can exhibit a topological band structure. However, while in fermionic systems the resulting gapless edge modes have a number of clear experimental signatures accessible through linear transport measurements, noninteracting bosonic systems with topological band structure have a simple condensate or the vacuum as their ground state, making it more difficult to ascertain their topological nature. Their excited states, however, may carry clear signatures of the topology of the band structure, for example in form of a thermal Hall response. Here we propose driving a topological magnetic insulator with an electromagnetic field and show that this causes edge mode instabilities and a large non-equilibrium steady-state magnon edge current. We discuss several ways how the edge current can be detected directly and reveal a driven Hall effect, techniques that allow to unambiguously establish the presence of edge modes in such materials. Based on our amplification mechanism we propose a topological travelling-wave amplifier and topological magnon laser with applications in magnon spintronics.

The effect of measurement on the time-evolution of a system is one of the most puzzling aspects of quantum dynamics, sharply distinguishing the latter from ist classical counterpart. One paradigmatic example is the quantum Zeno effect, whereby a frequent-enough measurement of a quantum system results in a localisation of its state in Hilbert space. The interplay between measurement and intrinsic quantum correlations in many-body systems can lead to novel collective phenomena, with the first few examples being discovered recently. In this work, we introduce the “quantum-Zeno Fermi polaron”: a quasi-particle emerging for lossy impurities immersed in a bath of fermions. For loss rates of the order of the impurity-fermion binding energy the polaron quasi-particle is very short lived. However, we show that in the Quantum Zeno limit of large loss rates a long-lived polaron branch re-emerges. This Quantum-Zeno Fermi polaron is not simply a copy of the original polaron in absence of losses, but rather originates from the nontrivial interplay between the Fermi-surface and the surface of the region forbidden by the quantum Zeno projection. This results for instance into a different dispersion law of this novel quasi-particle.

Universal quantum computers are potentially an ideal setting for simulating many-body quantum dynamics that is out of reach for classical digital computers. We use state-of-the-art IBM quantum computers to study paradigmatic examples of condensed matter physics – we simulate the effects of disorder and interactions on quantum particle transport, as well as correlation and entanglement spreading. Our benchmark results show that the quality of the current machines is below what is necessary for quantitatively accurate continuous time dynamics of observables and reachable system sizes are small comparable to exact diagonalization. Despite this, we are successfully able to demonstrate clear qualitative behaviour associated with localization physics and many-body interaction effects. Reference: arXiv:1906.06343.

The growth of entanglement during the non-equilibrium dynamics of quantum many-body systems constitutes a major challenge for numerical simulations on classical computers. We explore the possibility to compress the many-body wave function using artificial neural networks as a versatile approach for the efficient simulation of quantum dynamics. This method allows us to study two-dimensional systems far from equilibrium, which are realized, e.g., in quantum simulators based on cold atoms or Rydberg atoms. In our discussion we include subtleties of the time evolution algorithm, ways to assess the accuracy of the results, and the gain of an efficient implementation on a distributed memory machine with GPU acceleration.

Right at the interface between relativistic spin and fermionic physics lies the Gross Neveu Yukawa (GNY) field theory which is believed to capture the complex interplay of bosonic and fermionic quantum critical fluctuation in a class of universal critical exponents. We present quantum Monte Carlo simulations for the particularly challenging chiral Heisenberg GNY quantum phase transition of relativistic fermions with $N=4,\ldots 8$ Dirac spinor components subject to a repulsive local four fermion interaction in 2+1$d$, where non-perturbative methods are essential to no only sort out quantitative differences in the literature, but to tackle basic open questions of the underlying physics. Here we employ a two dimensional lattice Hamiltonian with a single, spin-degenerate Dirac cone, which exactly reproduces a linear energy-momentum relation for all finite size lattice momenta in the absence of interactions. This allows us to significantly reduce finite size corrections compared to the widely studied honeycomb and $\pi$-flux lattices. A Hubbard term dynamically generates a mass beyond a critical coupling as the system acquires antiferromagnetic order and SU(2) spin rotational symmetry is spontaneously broken. At the quantum phase transition we extract a self-consistent set of critical exponents and provide further evidence for the continuous degradation of the quasi-particle weight of the fermionic excitations and the regularity of the effective "speed of light" of the low-energy relativistic description as the critical point is approached. We complement our quantum Monte Carlo finite size scaling analysis with level spectroscopy guided by exact diagonalization and perturbation theory for the chiral Ising GNY quantum phase transition with $N=4$ Dirac spinor components in order to identify universal fingerprints of the critical field theory. Our investigation shows that precise knowledge of the spectrum even on small clusters already provides valuable insight into the properties of critical systems. We show that the strong interaction between the spinor field and the scalar order-parameter field strongly influences the critical energy levels on the torus.

Tensor network states and parton wave functions are two pivotal methods for studying strongly correlated systems. We connect these two subjects by demonstrating that a variety of parton wave functions, such as projected Fermi sea and projected fermionic/bosonic paired states, can be expressed as tensor network states. This further allows to compress projected wave functions into matrix product states and extract useful information for characterizing these wave functions. Several paradigmatic parton wave functions for spin-1/2 systems are tested to benchmark our method.

We study quantum quenches in the spin-1 Heisenberg spin chain and show that the dynamics can be described by the recently developed semi-semiclassical method based on particles propagating along classical trajectories but scattering quantum mechanically. We analyze the non-equilibrium time evolution of the distribution of the total spin in half of the system and compare the predictions of the semi-semiclassical theory with those of a non-Abelian time evolving block decimation (TEBD) algorithm which exploits the SU(2) symmetry. We show that while the standard semiclassical approach using the universal low energy scattering matrix cannot describe the dynamics, the hybrid semiclassical method based on the full scattering matrix gives excellent agreement with the first principles TEBD simulation.