Dynamical Probes for Exotic States of Matter

Subjecting a many-body localized system to a time-periodic drive generically leads to delocalization and a transition to ergodic behavior if the drive is sufficiently strong or of sufficiently low frequency. Here we show that a specific drive can have an opposite effect, taking a static delocalized system into the MBL phase. We demonstrate this effect using a one dimensional system of interacting hardcore bosons subject to an oscillating linear potential. The system is weakly disordered, and is ergodic absent the driving. The time-periodic linear potential leads to a suppression of the effective static hopping amplitude, increasing the relative strengths of disorder and interactions. Using numerical simulations, we find a transition into the MBL phase above a critical driving frequency and in a range of driving amplitudes. Our findings highlight the potential of driving schemes exploiting the coherent suppression of tunneling for engineering long-lived Floquet phases.

Dynamical correlation functions probe the excitations of a many-body system and therefore characterize quantum states. Moreover, out-of-time-ordered (OTO) correlation functions provide even further insights, as they describe scrambling of quantum information throughout the system. Here, we study the dynamical response of a diffusive quantum many-body system on the concrete example of the non-integrable, one-dimensional Bose-Hubbard model at high temperatures. Our numerical simulations show a ballistic behavior of the OTO correlators of massive particles even in a high temperature regime, where well-defined quasiparticles cease to exist and time-ordered correlation functions behave incoherently or diffusively. The slowest process in the global thermalization of the system is hence not the spread of quantum information, but the diffusion of conserved quantities. We furthermore develop an experimentally feasible protocol to overcome some of the challenges faced by existing proposals at finite temperatures and probe the behavior of time-ordered and out-of-time-ordered correlation functions.

When a Dirac semimetal is subject to a circularly polarized laser, it is predicted that the Dirac cone splits into two Weyl nodes and a nonequilibrium transient state called the Floquet Weyl semimetal is realized. We focus on the previously unexplored low frequency regime, where the upper and lower Dirac bands resonantly couples with each other through multi-photon processes, which is a realistic situation in solid state ultrafast pump-probe experiments. We find a series of new Weyl nodes emerging in pairs when the Floquet replica bands hybridize with each other. The nature of the Floquet Weyl semimetal with regard to the number, locations, and monopole charges of these Weyl nodes is highly tunable with the amplitude and frequency of the light. We derive an effective low energy theory using Brillouin-Wigner expansion and further regularize the theory on a cubic lattice. The monopole charges obtained from the low-energy Hamiltonian can be reconciled with the number of Fermi arcs on the lattice which we find numerically.

In this talk the quench dynamics and the generalized Gibbs ensemble for non-interacting topological systems will be discussed. Generally the topological systems behave in a very strange way. If the system is quenched cross the phase boundaries, the topology disappears as expected. However, if the system is quench in the same phase, most of the time the topology remains, however if it is too closed to the phase boundary, the topology still disappear. We are going to discuss this strange behavior in this talk.

We investigate charge relaxation in the spin-less disordered fermionic Hubbard chain (t−V-model). Our observable is the time-dependent density propagator, Π_ε(x,t), calculated in windows of different energy density, ε, of the many-body Hamiltonian and at different disorder strengths, W, not exceeding the critical value Wc. The width Δx_ε(t) of Π_ε(x,t) exhibits a behavior dlnΔx_ε(t)/dlnt=β_ε(t), where the exponent function β_ε(t)≲1/2 is seen to depend strongly on L at all investigated parameter combinations. (i) We cannot confirm the existence of a region in phase space that exhibits (genuine) subdiffusive dynamics in the sense that β_ε<1/2 is numerically fixed in the limit of large L. Instead, subdiffusion might possibly be transient, only, finally giving way to conventional diffusive behavior with β_ε=1/2. (ii) Similarly, we cannot confirm the existence of many-body mobility edges deep in the delocalized phase. (iii) (Transient) subdiffusion 0<β_ε(t)≲1/2, coexists with an enhanced probability for returning to the origin, Π_ε(0,t), decaying much slower than 1/Δx_ε(t). Correspondingly, the spatial decay of Π_ε(x,t) is far from Gaussian being exponential or even slower. On a phenomenological level, our findings are broadly consistent with effects of strong disorder and (fractal) Griffiths regions.

We investigate the stationary and dynamical behavior of a central spin Hamiltonian interacting with a random spin bath. We perform the Jordan-Wigner transformation to the mentioned Hamiltonian and split it into a non-interacting and an interacting parts. We see that the resulting dynamics can be mainly explained by means of the non-interacting dynamics, which eigenstates show a frozen spectrum of fractal dimension, which is characteristic for localized phases in models with power-law hoppings. For weak coupling strengths to the central spin, we identify a regime where transport of particles and information behaves logarithmic in time.

Luttinger liquids (LLs) arise by coupling left- and right-moving particles through interactions in one dimension. This most natural partitioning of LLs is investigated by the momentum-space entanglement after a quantum quench using analytical and numerical methods. We show that the momentum-space entanglement spectrum of a LL possesses many universal features both in equilibrium and after a quantum quench. The largest entanglement eigenvalue is identical to the Loschmidt echo, i.e. the overlap of the disentangled and final wavefunctions of the system. The entanglement gap is universal both in equilibrium and after a quantum quench. The momentum-space entanglement entropy is always extensive and saturates fast to a time independent value after the quench, in sharp contrast to a spatial bipartitioning.

Much of the recent work on Floquet systems have focused on 2-band models. However, in solid state systems multi-band systems are ubiquitous. In this talk, I present the results of 3-band and 4-band systems under a periodic drive. Both systems are chosen to have Dirac points and quadratic band touching points in their band structure. Surprisingly, the response of the bands to the periodic drive can be rather different in 2-band, 3-band, and 4-band models, which has implications for experimental realizations of Floquet systems in the solid state. In addition we compute the optical conductivity of the multi-band systems. If time permits, I will also discuss recent work on the short-to-intermediate time evolution of periodically driven interacting systems.

Systems where all energy eigenstates are localized are known to display an emergent local integrability, in the sense that one can construct an extensive number of operators that commute with the Hamiltonian and are localized in real space. Here we show that emergent local integrability does not require a complete set of localized eigenstates. Given a set of localized eigenstates comprising a nonzero fraction (1−f) of the full many body spectrum, one can construct an extensive number of integrals of motion which are local in the sense that they have {\it nonzero weight} in a compact region of real space, in the thermodynamic limit. However, these modified integrals of motion have a `global dressing' whose weight vanishes as ∼f as f→0. In this sense, the existence of a {\it non-zero fraction} of localized eigenstates is sufficient for emergent local integrability. We discuss the implications of our findings for systems where the spectrum contains delocalized states, for systems with projected Hilbert spaces, and for the robustness of quantum integrability.

Quantum phase transition is a ground-state phenomenon where the phases are characterized by ordering (long-range/topological) of the ground state of a many-body Hamiltonian as a function of the parameters of the Hamiltonian. Sharp changes in physical properties (order parameters) and entailing singularities are observed at the transition point as one follows the ground state as a function of parameters. As energy is increased, however, the ordering is destroyed, and the concept of phase transition is obscured. For example, in one dimensional systems the order is absent in any state with finite energy density. Here we demonstrate that signature of ground state quantum phase transitions are nonetheless hidden even in highly excited non-equilibrium states with finite energy densities. We demonstrate this for integrable model as well as generic interacting models in which both conventional and topological quantum phase transitions are well studied. The signature can be employed in locating the quantum critical point precisely in the parameter space.

The asymptotic state of a periodically driven many-body quantum system in contact with an environment is investigated. The combined action of the driving and the environment steers the system towards a state being characterized by a time-periodic density operator. To compute this asymptotic non-equilibrium state at stroboscopic instants of time, we introduce the dissipative Floquet map, find the stroboscopic density operator as its eigen-operator and demonstrate how particle interactions affect properties of the density operator. We illustrate the idea with a periodically rocked open Bose-Hubbard dimer and discuss the relations between the interaction-induced bifurcation transitions in a mean-field dynamics and changes in the characteristics of the quantum many-body state. We argue that Floquet maps can provide insight into the system relaxation towards its asymptotic state and may help to identify the stroboscopic time-independent generator mimicking the action of the original time-dependent one.

Many-body localized phases occur in interacting systems and are characterized by the absence of transport, the lack of thermalization, as well as the existence of quasi local integrals of motions. Ultra cold atoms have proven to be an ideal experimental test bed to test theoretical predictions. Most of the experiments involve the real time evolution of an initial state prepared by sudden changes in system parameters. First, we numerically investigate signatures of many body localization by studying the melting of a domain wall after a quantum quench [1]. Second, we consider a dynamical system in which we couple initially hot and cold regions. We show that it is possible to extract characterizing properties like the localization length and the critical disorder strength. [1] J. Hauschild et al., Phys. Rev. B 94, 161109(R)

We show the persistance of toplogically protected charge pumping in the presence of strong interactions for 1D systems. We demonstrate the existance of a phase transition in which the pumping breaks down through DMRG computations, and discuss the scaling behaviour at this transition.

We investigate the stationary and dynamical behavior of an Anderson localized chain coupled to a single central bound state. The presence of the central site leads to a mixing of Anderson localized states, but fails to delocalize the system. In particular, the number of resonantly coupled sites remains nite in the thermodynamic limit. This is further supported by a multifractal analysis of eigenstates that shows the frozen spectrum of fractal dimension, which is characteristic for localized phases in models with power-law hopping. Although the well-known Fano-resonance problem is seemingly similar to our system, it fails to describe it because of the absence of level repulsion within the energy spectrum. For weak coupling strengths to the central site, we identify a regime with a logarithmic in time transport of particles and information.

Light cone spreading of correlations and entanglement is a key feature of the non-equilibrium quench dynamics of many-body quantum systems. First proposed theoretically, it has been experimentally revealed in cold-atomic gases and it is expected to be a generic characteristic of any quench in systems with short-range interactions and no disorder. Conversely, here we propose a mechanism that, through confinement of the elementary excitations, strongly suppresses the light-cone spreading. Confinement is a celebrated concept in particle physics, but it also exists in condensed matter systems, most notably in one spatial dimension where it has been experimentally observed. Our results are obtained for the Ising spin chain with transverse and longitudinal magnetic field, but the proposed mechanism is of general validity since it is based on the sole concept of confinement and it should be easily observed in cold atom experiments. /M. Kormos, M. Collura, G. Takács, P. Calabrese, Nature Physics, Advanced Online Publication: http://www.nature.com/articles/nphys3934/

Angle-resolved photoemission spectroscopy (ARPES) has so far been the definitive method for the characterization of materials as topological semimetals, via direct visualization of band touchings in the bulk and nontrivial states at the boundary. However, several unconventional and potentially useful properties of topological semimetals appear only in sizable electromagnetic fields, which severely limit the resolving power of ARPES. The controlled splitting of Dirac nodes to nondegenerate Weyl nodes in Dirac semimetals and the chiral anomaly in Weyl and Dirac semimetals are important examples of such unique properties. We show how resonant inelastic x-ray scattering (RIXS) offers a viable path for the spectroscopic detection of the aforementioned effects. By low-energy modeling of specific material candidates based on ab initio band structure calculations, we derive the corresponding RIXS spectra and highlight the salient features stemming from topological nontriviality. The proposed measurements are within the resolving capabilities of current instrumentation.

We present a model of a topological semimetal in three dimensions (3D) whose energy spectrum exhibits a nodal line acting as a vortex ring; this in turn is linked by a pseudospin structure akin to that of a smoke ring. Contrary to a Weyl point node spectrum, the vortex ring gives rise to skyrmionic pseudospin patterns in cuts on both sides of the nodal ring plane; this pattern covers the full Brillouin zone, thus leading to a new, `maximal', anomalous Hall effect in a 3D semimetal. Tuning a model parameter shrinks the vortex ring until it vanishes, giving way to a pair of Weyl nodes of opposite chirality. This establishes a connection between two distinct momentum-space topologies - that of a vortex ring (a circle of singularity) and a monopole-anti-monopole pair (two point singularities). We present the model both as a low-energy continuum and a two-band tight-binding lattice model. Its simplicity permits an analytical computation of its Landau level spectrum. Ref: L.-K. Lim and R. Moessner, Phys. Rev. Lett. 118, 016401 (2017)

In order to measure the spread of information in a system of interacting fermions with nearest-neighbour couplings and strong bond disorder, one could utilise a dynamical real space renormalisation group (RG) approach on the spin-1/2 XXZ chain [1]. Under such a procedure, one sees that a many-body localised state is established as an infinite randomness fixed point and the entropy scales with time as log(log(t)). One interesting further question that results from such a study is the case when the Hamiltonian explicitly depends on time. This can be accomplished through the introduction of a time dependence in the couplings and bonds strengths and thus represents a further time scale within the problem. Here we answer this question by considering a dynamical renormalisation group treatment [1,2,3] on the strongly disordered random spin-1/2 XXZ chain [1] where the couplings are time-dependent and chosen to reflect a (slow) evolution of the governing Hamiltonian. Under the condition that the renormalisation process occurs at fixed time, a set of coupled second order, nonlinear PDE's can be written down in terms of the random distributions of the bonds and fields. Solution of these flow equations at the relevant critical fixed points leads us to establish the dynamics of the flow as we sweep through the quantum critical point of the Hamiltonian. We will present these critical flows as well as discussing the issues of duality, entropy and many-body localisation, before making connections to quantum adiabatic computations. Joint work with J. Betouras and A. Zagoskin [1] R. Vosk \& E. Altman, Phys. Rev. Lett. \textbf{110}, 067204 (2013). [2] D.S. Fisher, Phys. Rev B \textbf{51}, 6411 (1995). [3] C. Dasgupta \& S. Ma, Phys. Rev. B \textbf{22}, 1305 (1980).

We study photo-induced topological transitions in 2D materials with spin-orbit coupling. The examples for such materials are silicene, germanene and stanene where the Hamiltonian is Dirac like and driven periodically by an incident laser. The system is studied in a high-frequency limit using expansion based on the Brillouin-Wigner perturbation theory. The effective Hamiltonian thus computed has new terms renormalizing the bare Hamiltonian as well as new longer ranged couplings. We calculated the phase diagram using the effective Hamiltonian and compared with that of direct numerical computations. It is found that at high enough frequencies, the high energy expansion gives accurate results

Genons, i.e., dislocations in fractional Chern insulators with higher Chern number bands have been identified as non-Abelian defects [1]. So far, there has not been a convincing numerical demonstration of this effect, due to the enhanced complexity of simulating models without translational symmetry. Here, we report a detailed numerical study of a lattice model with a local Hamiltonian that stabilises genon defects. We provide direct evidence for their non-Abelian statistics by counting the associated quasiparticle degeneracies [2]. [1] M. Barkeshli & X.-L. Qi, Phys. Rev. X 2, 031013 (2012). [2] Z. Liu, G. Möller, E. Bergholtz, in preparation.

We propose a quite general approach, utilizing conformal field theory, to construct lattice models displaying the fractional quantum Hall effect. By adiabatically changing the coupling strengths in the Hamiltonian, it is possible both to create and destroy anyons in the ground states of these models and to move the anyons around in a controlled manner. Monte Carlo simulations allow us to get a detailed insight into the properties of the anyons, including their shape, charge, and braiding statistics. In addition, we show that in lattices quasielectrons can be constructed as the inverse of quasiholes. This is surprising since it is much harder mathematically to add quasielectrons than quasiholes in the standard fractional quantum Hall effect. Finally, we propose to use the introduction of anyons in wavefunctions as a probe for topological order, and we demonstrate how one can interpolate between lattice and standard fractional quantum Hall states. References: - Phys. Rev. B 91, 041106(R) (2015) - Phys. Rev. B 94, 245104 (2016) - arXiv:1609.02389

The effect of strong laser on quantum systems and its interplay with topology continues to be a hot topic. It is needless to say that the quantum Hall effect realized in the two dimensional electron gas (2DEG) subject to magnetic fields has provided a setup to deeply understand the concept of topology in condensed matter systems. Here, we ask the following question. “Does the 2DEG show Landau quantization in an oscillating magnetic field?” For a simple one particle Hamiltonian, we obtain a positive result [1]. Indeed, when the cyclotron frequency (proportional to the magnetic field strength) and the oscillating frequency takes a certain ratio, we obtain macroscopically degenerate Floquet bands just as in conventional Landau quantization. Then, the next natural question is to ask if the system shows Hall response. The answer is partially yes. When applied with an electric field, there will be a perpendicular current, but they will have different frequency mode. For example, if an ac-electric field is applied, there will be a dc-Hall current. A device that shifts the frequencies of the input and output signals is called a heterodyne, and thus we name this effect the heterodyne Hall effect. As for any relation with topology and bulk edge correspondence, we do not have an answer at this point. [1] T. Oka and L. Bucciantini, Phys. Rev. B. B 94, 155133 (2016)

Long time dynamics of non-integrable systems holds the key to fundamental questions (thermalization). Analytical tools can only apply to particular cases (integrable models, perturbative regimes). Numerical simulations, limited in time, have found evidence of different time scales. A new numerical technique for constructing slowly evolving local operators was introduced by Kim et al. in Phys. Rev. E 92, 012128 (2015). Those operators have a small commutator with the Hamiltonian and they might give rise to long time scales. In this work, we apply those techniques to the many body localisation phase transition. We show evidences for the presence of a sub-diffusive phase between the ergodic and the localised ones. We also propose a statistical interpretation of the Griffith singularities that emerge in proximity to the phase transition point.

We show that, in the presence of a $\pi/2$ artificial gauge field per plaquette, Mott insulating phases of ultracold fermions with SU($N$) symmetry and one particle per site generically possess an extended chiral phase with intrinsic topological order characterized by an approximate ground space of $N$ low-lying singlets for periodic boundary conditions, and by chiral edge states described by the SU($N$)$_1$ Wess-Zumino-Novikov-Witten conformal field theory for open boundary conditions. This has been achieved by extensive exact diagonalizations for $N$ between 3 and 9, and by a parton construction based on a set of $N$ Gutzwiller projected fermionic wave functions with flux $\pi/N$ per triangular plaquette. Experimental implications are briefly discussed.

Time-periodically driven cold atom systems are versatile toolboxes for realizing artificial gauge fields in quantum simulations. Great progress has been made in simulating topologically non-trivial models such as the Hofstadter- and Haldane-Hamiltonians. Up to now most experiments focus on the non-interacting regime. Introducing interactions into systems with artificial gauge fields will be of high interest. Floquet DMFT is a non-perturbative method to study the non-equilibrium steady state in interacting time-periodically driven systems. Using its generalization to real-space Floquet DMFT for inhomogeneous systems we studied the spectral function of the Hofstadter-Falicov-Kimball Hamiltonian and its realization in a time-periodically driven system. We calculated the effect of interactions on edge states in this system and discuss possible ways to observe them in experiments. We also discuss the possibility to study spectral functions of the Hofstadter-Hubbard Hamiltonian in time-periodically driven systems.

It is a well-known phenomenon that lattice systems exhibit an emergent light-cone structure, wherein the support of an operator in the Heisenberg picture grows linearly in time. However, much less is known about the internal structure of the light-cone. For ergodic systems, it is expected that the inside of the light-cone is essentially featureless, i.e. all operators that have support inside it have roughly equal contributions. This conjecture also has important consequences regarding the spreading of entanglement after a quantum quench. In this work we investigate the internal structure of the light-cone in detail. As a special case we treat time evolution under randomly chosen two-site unitary gates. This possesses the locality required for light-cone spreading, but has no additional constraints, and is therefore an extreme case of an ergodic system. In this case we are able to derive exact predictions for the spreading of operators, via a mapping to a two-dimensional classical spin system. We compare these with numerical results for different ergodic systems, obtained through tensor network methods.

Despite large quantum fluctuations, the ground state of the spin-1/2 triangular Heisenberg model has long-range order. The theoretical study of the $J_1 - J_2$ model has shown the existence of a quantum spin liquid phase for a finite interval of the next-nearest neighbor interaction $J_2$. Motivated by the recent experimental observation of a spin liquid phase in the triangular compound YbMgGaO4, we extend the $J_1 - J_2$ phase diagram to anisotropic spin-orbit interactions relevant for this material. Our study is based on the analysis of the ground state obtained using infinite DMRG. Using a recently developed DMRG time-evolution scheme, we also obtain the dynamic structure factor in the different phases.

We construct effective potentials for non-equilibrium quantum many-body systems, analogous to thermodynamic potentials in equilibrium statistical mechanics. These potentials encode the dynamical behaviour of macroscopic observables, providing an ideal framework for the study of eigenstate-ordered phases and transitions between them. We demonstrate this for many-body localised and Ising spin glass systems.

Two-dimensional (2D) semi-Dirac materials are characterized by a quadratic dispersion in one direction and a linear dispersion along the orthogonal direction. We study the topological phase transition in such 2D systems in the presence of an electromagnetic field. We show that a Chern insulating state emerges in a semi-Dirac system with two gapless Dirac nodes in the presence of light. In particular, we show that the intensity of a circularly polarized light can be used as a knob to generate topological states with nonzero Chern number. In addition, for fixed intensity and frequency of the light, a semi-Dirac system with two gapped Dirac nodes with trivial band topology can reveal the topological transition as a function of polarization of the light.

We study the Hall conductance of topological insulators in the long time limit after a global quench of the Hamiltonian and identify a topologically driven nonequilibrium phase transition. This phase transition is indicated by the nonanalyticity of the Hall conductance as a function of the quench parameter. The non-analytic behaviour is universal in two-band Chern insulators such as the Dirac model, the Haldane model, or the Kitaev honeycomb model. Their realisation as effective Hamiltonians of a periodically driven system leads to slight modifications of the non-analytic behaviour.

We consider a system of non-interacting fermions in one dimension subject to a single-particle potential consisting of (a) a strong optical lattice, (b) a harmonic trap, and (c) uncorrelated on-site disorder. After a quench, in which the center of the harmonic trap is displaced, we study the occupation function of the fermions and the time-evolution of experimental observables. Specifically, we present numerical and analytical results for the post-quench occupation function of the fermions, and analyse the time-evolution of the real-space density profile. Unsurprisingly for a non-interacting (and therefore integrable) system, the infinite-time limit of the density profile is non-thermal. However, due to Bragg-localization of the higher-energy single-particle states, the approach to even this non-thermal state is extremely slow. We quantify this statement, and show that it implies a sensitivity to disorder parametrically stronger than that expected from Anderson localization.

We classify Floquet states using a simple algorithm, matching the more elaborate underlying mathematical procedures from an easy implementable perspective.

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 a quenched disorder, 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.

Sodium Iridate compounds of the form $Na_{2}IrO_{3}$ are known to be magnetically ordered and show residual spin liquid behaviour at high temperatures. The Kitaev-Heisenberg model has been a strong contender for describing such systems. We decoupled the model using the Majorana mean field, thus allowing for both short range correlations and magnetic order. We first located a regime in parameter space where short-range correlations exist despite the magnetic order being non-zero. This is the zigzag phase with short range correlations. In this regime, close to the spin liquid boundary, that we computed the Raman Response for the model at zero temperature and found a broad band which is a signature of short range correlations. We found our results to be in good agreement with the experiments. On the other hand in $Na_{4}Ir_{3}O_{8}$ no magnetic order was found down to 100 mK. Our calculations of the Raman response of the Kitaev-Heisenberg model on the hyperkagome lattice shows that the experimental observations are consistent with the calculated Raman response where the Kitaev exchange interaction ($J_K$) is much larger than the Heisenberg term $J_1$ ($J_{1}/J_{K}∼0.1$).

Topological state of matter is a new paradigm in the modern condensed matter physics [1]. Topologically non-trivial superconducting state attracts particular interest because it provides a platform to host a Majorana fermion [2]. However, the topological superconducting state (TSC) has not yet been evidenced in natural superconducting systems, although a few indications have been obtained in artificial systems by state-of-the-art experiments [3, 4]. On the other hand, in recent years, tremendous developments have been achieved in the realization of topological phases by laser light applications [5, 6]. Laser-irradiated systems reach nonequilibrium steady states, which cannot be realized in equilibrium states. Thus the laser light is a new tool for controlling the topological states of matter. In this seminar, we propose a possible way to realize topological superconductivity with application of laser light to superconducting cuprate thin films [7]. Applying Floquet theory to a model of d-wave superconductors with Rashba spin-orbit coupling, we derive the effective model and discuss its topological nature. Interplay of the Rashba spin-orbit coupling and the laser light effect induces the synthetic magnetic fields, thus making the system gapped. Then the system acquires the topologically non-trivial nature. The synthetic magnetic fields do not create the vortices in superconductors, and thus the proposed scheme provides a promising way to dynamically realize a topological superconductor in cuprates. We also discuss experiments to detect the signature. References: [1] X.-L. Qi and S.-C. Zhang, Rev. Mod. Phys. 83, 1057 (2011) [2] M. Sato and S. Fujimoto, J. Phys. Soc. Jpn. 85, 072001 (2016) [3] V. Mourik, et al. Science 336, 1003 (2012) [4] S. Nadj-Perge, et al. Science 346, 602 (2014) [5] T. Oka and H. Aoki, Phys. Rev. B 79, 081406 (2009). [6] N. H. Lindner, G. Refael, and V. Galitski, Nat. Phys. 7, 490 (2011). [7] K. Takasan, A. Daido, N. Kawakami and Y. Yanase arXiv: 1612.01596

Heavy transition metals ($5d$) and rare-earth ions ($4f$) entail strong spin-orbit coupling that renders magnetic interactions anisotropic. This creates new mechanisms of magnetic frustration that 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$_4$. Ba$_3$InIr$_2$O$_9$ contains Ir-Ir dimers arranged on a triangular lattice. Each dimer hosts one unpaired electron resulting in an effective j=1/2 physics. Using neutron scattering, NMR, and muSR we demonstrate that this material is free from structural disorder and shows dynamic behavior down to at least 25 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 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. muSR confirms the absence of magnetic ordering or spin freezing down to at least 50 mK. The possible spin Hamiltonian for this material will be discussed.

We consider the fate of a helical edge state of a spin Hall insulator and its topological transition in presence of a circularly polarized light when coupled to various forms of environments. A Lindblad type equation is developed to determine the fermion occupation of the Floquet bands. We find by using nalytical and numerical methods that non-secular terms, corresponding to 2-photon transitions, lead to a mixing of the band occupations, hence the light induced photocurrent is in general not perfectly quantized in the presence of finite coupling to the environment, although deviations are small in the adiabatic limit. Sharp crossovers are identified at driving frequencies near the Rabi frequency $\Omega$ (which is the strength of light-matter coupling) and at $\frac{1}{2}\Omega$ with the former resembling to a phase transition.

Co-authors: Matthias Gohlke, Roderich Moessner, Frank Pollmann 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 $\alpha$-RuCl$_3$, where we find high energy features seen in inelastic neutron scattering experiments. Our results provide an example of a natural path for proximate spin liquid features to arise at high energies above a conventionally ordered state, as the diffuse remnants of spin-wave bands intersect to yield the observed robust peak at the Brillouin zone center.

Emergent states of matter in quantum magnets are characterized by their elementary magnetic excitations that can be induced and tuned in an external magnetic field. We report on terahertz spectroscopy of elementary excitations in a spin-1/2 Heisenberg-Ising antiferromagnetic chain as a function of temperature and magnetic field. At zero field confined spinon excitations are observed below the Néel temperature [1]. Emergent ferminonic excitations are observed in a transverse magnetic field [2], when the confinement is suppressed and an order-disorder phase transition is induced. In the longitudinal fields, the high-energy string excitations are observed in addition to the low energy spin exciations. These experimental results are understood by comparison to precise calculation of dynamic structure factors by the method of infinite time evolving block decimation and using Bethe ansatz for the transverse and longitudinal fields, respectively. In collaboration with Anup Kumar Bera, Joachim Deisenhofer, Hans Engelkamp, Papori Gogoi, A. T. M. Nazmul Islam, Dmytro Kamenskyi, Bella Lake, Alois Loidl, Michael Schmidt, Nanlin Wang, Congjun Wu, Jianda Wu, Shenglong Xu, Wang Yang. [1]ZW et al. Phys. Rev. B 91, 140404(R) (2015). [2]ZW et al. Phys. Rev. B 94, 125130 (2016).

In this work we employ a quantum Monte Carlo approach to the extended square-lattice Hubbard model at half-filling. Using the particle-hole symmetry, one is able to construct a positive-definite path integral formulation of the problem which allows the use of efficient sampling algorithms commonly used in lattice quantum chromodynamics. With this fully nonperturbative setup, we study the formation of Hubbard bands and the unusual features of the collective charge excitations that result. Using our Euclidean time, Monte Carlo data we employ a novel variant of the Backus-Gilbert method for numerical analytic continuation to obtain both one-particle and two-particle spectral functions. In particular, we used this procedure to compute the density of states and the dispersion relation for plasmons in the strongly-correlated regime. Through this approach, we obtain a well-defined and robust procedure which can be used by practitioners of various numerical approaches to strongly-correlated problems.