New Trends in Nonequilibrium Many-Body Systems: Methods and Concepts

Recent progress in laser technologies enables the study of highly nonlinear optical phenomena in systems ranging from gases to solids. High-harmonic generation (HHG) is a prominent example with important technological applications. In the last decade, the scope of HHG research has been extended from gases to solids, in particular to semiconductors. HHG in semiconductors can be well described by the dynamics of independent electrons, which enables the HHG spectroscopy of band information such as dispersion relations and Berry curvatures. The HHG spectroscopy also has a significant potential in the study of strongly correlated materials, where it may detect the dynamics of many-body states [1,2] as well as photo-induced phase transitions. However, the underlying mechanism of HHG in strongly correlated systems (SCSs) is poorly understood so far. In particular, the role of strong correlations between different degrees of freedom, such as spin and charge, in highly nonlinear optical responses has not been explored, even though such correlations are an essential hallmark of SCSs. In this talk, we theoretically show that strong spin-charge coupling leads to characteristic behavior of nonlinear optical phenomena which is completely opposite to that expected in conventional semiconductors [3]. We numerically analyze HHG in Mott insulators with antiferromagnetic correlations. We find a drastic enhancement of the HHG intensity and the cutoff energy with decreasing temperature, even though the band gap increases and the production of charge carriers is strongly suppressed. These results are consistent with recent HHG experiments on the Mott insulator Ca2RuO4, while in semiconductors, the increase of the gap would result in a suppressed HHG signal [4]. We reveal that this anomalous behavior originates from the strong spin-charge coupling in Mott insulators and its cooperation with thermal fluctuations. Our results suggest that the peculiar behavior of HHG is a generic feature in Mott insulators, which can be controlled via the Coulomb interaction and dimensionality of the system. Furthermore, the enhancement of HHG is a fingerprint of the spin-charge coupling, which may be utilized as a measure for the strength of the correlation in materials. [1] Y. Murakami, M. Eckstein and P. Werner, PRL 121, 057405 (2018). [2] Y. Murakami, S. Takayoshi, A. Koga, and P. Werner, PRB 103, 035110 (2021). [3] Y. Murakami, K. Uchida, A. Koga, K. Tanaka and P. Werner, arXiv: 2203.01029 (2022). [4] K. Uchida, et.al., arXiv:2106.15478 (PRL accepted).

Numerically exact real time quantum Monte Carlo methods simulate steady state dynamics by propagating a tractable initial condition to long times. Though inchworm algorithms make this tractable, the computational cost for accurately accessing nonequilibrium steady states often remains prohibitive. We overcome this issue by reformulating the inchworm equations directly in the steady state. We validate the resulting method against analytic results and other numerically exact techniques, and discuss applications to extended correlated systems by way of the dynamical mean field theory.

We present a toolbox of Non-Equilibrium Green's Function methods to simulate the correlated dynamics of interacting electrons and phonons and/or photons. All methods scale linearly in time and they are particle and energy conserving. We discuss recent applications on the ultrafast charge migration processes in organic molecules ionized by attosecond laser pulses, the relaxation dynamics of optically excited semiconductors and the phenomenon of carrier multiplication in photo-excited graphene.

The hierarchical equations of motion (HEOM) approach is a numerically exact method to studying the dynamics of open quantum systems with non-perturbative system-environment interaction and non-Markovian memory at finite temperatures. Although considerable progress has been made over the past few decades to extend the applicability of the HEOM approach, the numerical cost is still very expensive for reasonably large systems. In this contribution, we present the twin-space formulation of the HEOM approach in combination with the matrix product state representation for open quantum systems coupled to a hybrid fermionic and bosonic environment. The key ideas of the approach are a reformulation of a set of differential equations for the auxiliary density matrices into a time-dependent Schrödinger-like equation for an augmented multi-dimensional wave function as well as its tensor decomposition into a product of low-rank matrices. The new approach facilitates accurate simulations of non-equilibrium quantum dynamics in larger and more complex open quantum systems with both factorized and correlated initial conditions. The performance of the method is demonstrated for a model of a molecular junction exhibiting current-induced mode-selective vibrational excitation.

Describing a quantum impurity coupled to one or more non-interacting fermionic reservoirs is a paradigmatic problem in quantum many-body physics. While historically the focus has been on the equilibrium properties of the impurity-reservoir system, recent experiments with mesoscopic and cold-atomic systems enabled studies of highly non-equilibrium impurity models, which require novel theoretical techniques. We propose an approach to analyze impurity dynamics based on the matrix-product state (MPS) representation of the Feynman-Vernon influence functional (IF). The efficiency of such a MPS representation rests on the moderate value of the temporal entanglement (TE) entropy of the IF, viewed as a fictitious "wave function" in the time domain. We obtain explicit expressions of this wave function for a family of one-dimensional reservoirs, and analyze the scaling of TE with the evolution time for different reservoir's initial states. While for initial states with short-range correlations we find temporal area-law scaling, Fermi-sea-type initial states yield logarithmic scaling with time, closely related to the real-space entanglement scaling in critical 1d systems. Furthermore, we describe an efficient algorithm for converting the explicit form of the reservoirs' IF to MPS form. Once the IF is encoded by a MPS, arbitrary temporal correlation functions of the interacting impurity can be efficiently computed, irrespective of its internal structure. The approach introduced here can be applied to a number of experimental setups, including highly non-equilibrium transport via quantum dots and real-time formation of impurity-reservoir correlations.

Describing the real-time dynamics of interacting quantum many-body systems is a formidable challenge. Green's function based methods can be readily extended to real-time dynamics by using the Kadanoff-Baym real-time contour Green's function formalism [1], where the components of the Green's function acquire two independent time arguments. Numerical simulations require some form of discretization of the time dependence, and straight forward equidistant time grid has been successfully used for small model systems [2]. For a given discretization, the second challenge is to develop robust and accurate numerical algorithms for solving the Dyson equation of motion for the Green's function. In this talk I will present progress on both these aspects. The discrete Lehmann representation (DLR) [3] is a new discretization scheme for the imaginary time branch with asymptotic optimal scaling and analytic basis functions. The DLR has logarithmic scaling of the number of discretization points with respect to the inverse temperature, a drastic improvement compared to the equidistant grid exhibiting linear scaling. By combining the DLR with an equidistant real-time grid we have developed a fast equilibrium real-time solver for the Dyson equation [4], where the real-time history integral is evaluated using FFT, enabled by a hierarchical decomposition of the convolution matrix. This enables the study of both low temperature and low energy phenomena like the low frequency square root divergence in the Sachdev-Yitaev-Ke model. [1] G. Stefanucci and R. van Leeuwen, Nonequilibrium Many-Body Theory of Quantum Systems A Modern Introduction, Cambridge University Press (2013) [2] M. Schüler, et al., Comput. Phys. Commun., v257, 107484 (2020) [3] J. Kaye, et al., arXiv:2107.13094, J. Kaye, K. Chen, HURS, arXiv:2110.06765 [4] J. Kaye, HURS, arXiv:2110.06120

The concept of polarons -- quasiparticles formed by mobile impurities interacting with a reservior of particles -- has proven invaluable in equilibrium physics. Recently solid-state and cold atom experiments have begun to explore polaron dynamics far from equilibrium, creating the need to extend the theoretical description to this regime. However, the description of the time evolution following a sudden quench or excitation by a laser pulse is challenging as one has to capture both the violent intial dynamics as well as the eventual thermalization at long times driven by the strong interactions with the reservoir. In this talk I will discuss the description of polaron dynamics in terms of non-equilibrium Green's functions. I will begin with an intuitive quantum kinetic equation before switching to a more quantitative approach, assuming nothing but low polaron densities. Both methods are compared with recent experiments in cold atoms and transition metal dichalcogenide (TMD) monolayers.

I will show how one can harness symmetry and dynamical control to maximally entangle two distant parts of an interacting many-body system. The approach consists of applying timed pulses to drive a system to a desired symmetry sector with maximal bipartite long-range entanglement. As a concrete example, I will demonstrate how a simple sequence of on-site pulses on a qubit array can efficiently produce multiple stable nonlocal Bell pairs, realizable in existing atomic and photonic platforms. More generally, the approach provides a way to prepare exotic quantum correlations. For instance, I will discuss how it allows the creation of long-sought-after superconducting $\eta$ pairs in a repulsive Hubbard model.

Well-controlled synthetic quantum systems, such as ultracold atoms in optical lattices, offer intriguing possibilities to study complex many-body problems in regimes that are beyond reach using state-of-the-art classical computations. The basic idea is to construct and use a well-controlled quantum many-body system in order to study its in- and out-of-equilibrium properties and potentially use it to develop more efficient tailored numerical methods that can then be applied to other systems that are not directly accessible with the simulator. An important future quest concerns the development of novel experimental techniques that allow us to expand the range of models that can be accessed. I will demonstrate this using the example of topological lattice models, which in general do not naturally appear in cold-atom experiments. I will show how the technique of periodic driving, also known as Floquet engineering, facilitates their realization and show how charge-neutral atoms in lattices can mimic the behavior of charged particles in the presence of an external magnetic field. A key ingredient for quantum simulation is the degree of control one has over the individual particles and the microscopic parameters of the model. We have recently succeeded to not only use the technique of periodic driving to emulate physical systems that we know exist in nature, but to take this idea one step further and realize completely new topological regimes that do not have any static analog. Moreover, we are currently developing a novel hybrid optical lattice platform, where tightly focused optical tweezers are used to locally control the motion of the atoms in the lattice, paving the way towards quantum simulation of simplified lattice gauge theories, which play a fundamental role in a variety of research areas including high-energy physics and topological quantum computation.

Understanding intertwined orders with competing degrees of freedom is one of the most challenging problems in strongly correlated systems. We present a generic procedure for quantifying the interplay of electronic and lattice degrees of freedom in photo-doped insulators through a comparative analysis of theoretical many-body simulations and time- and angle-resolved photoemission spectroscopy (TR-ARPES) of the transient response of the candidate excitonic insulator Ta2NiSe5. The new paradigm is that lifetime changes after a photo-excitation carry essential information about the competition between active degrees of freedom. We will exemplify the concept on the excitonic insulator candidate Ta2NiSe5, where the interplay between electronic and lattice degrees of freedom is a matter of hot debate. The distinction between electron-driven versus lattice-driven situations is apparent as in the former, the photo-induced lifetime changes are substantial, while in the latter, they are strongly suppressed. The quantitative comparison between experiment and theory demonstrates the pivotal (but not necessarily sole) contribution of electron-electron interactions to stabilizing the electronic gap in the material.

I present a new computational paradigm to simulate time and momentum resolved inelastic scattering spectroscopies in correlated systems. The conventional calculation of scattering cross sections relies on a treatment based on time-dependent perturbation theory, that provides formulation in terms of Green’s functions. In equilibrium, it boils down to evaluating a simple spectral function equivalent to Fermi’s golden rule, which can be solved efficiently by a number of numerical methods. However, away from equilibrium, the resulting expressions require a full knowledge of the excitation spectrum and eigenvectors to account for all the possible allowed transitions, a seemingly unsurmountable complication. Similar problems arise when the quantity of interest originates from higher order processes, such as in Auger, Raman, or resonant inelastic X-ray scattering (RIXS). To circumvent these hurdles, we introduce a time-dependent approach that does not require a full diagonalization of the Hamiltonian: we simulate the full scattering process, including the incident and outgoing particles (neutron, electron, photon) and the interaction terms with the sample, and we solve the time-dependent Schrödinger equation. The spectrum is recovered by measuring the momentum and energy lost by the scattered particles, akin an actual energy-loss experiment. The method can be used to study transient dynamics and spectral signatures of correlation-driven non-equilibrium processes, as I illustrate with several examples and experimental proposals using the time-dependent density matrix renormalization group method as a solver. Even in equilibrium, we find higher order contributions to the spectra that can potentially be detected by modern instruments.

TBA

We establish the nonequilibrium thermal phases of a voltage driven antiferromagnetic Mott insulator in three dimensions, realised at steady state under a voltage bias. Starting from the Keldysh action for the half filled Hubbard model we derive an effective Langevin equation for the `slow' magnetic variables. The coupling of electrons to these degrees of freedom determine the transport properties. At low temperature we find a voltage-driven discontinuous insulator-metal transition, along with hysteresis. We map the suppression of the Néel temperature $T_N$ and pseudogap temperature $T_pg$ with increasing voltage, and discover that the biased Mott insulator has a finite temperature insulator-metal transition. The low temperature results resolve an experimental puzzle about hysteresis, and the thermal results make testable predictions on spectra and nonlinear transport.

We examine the nonequilibrium optical response of the one-dimensional half-filled extended Hubbard model to a pump field pulse. Using time-dependent density matrix renormalization group, we compute the differential optical conductivity and detect a concurrent photoexcitation of doublons and holons along with a reduction of the local magnetic moment and antiferromagnetic correlations. The differential optical conductivity exhibits two main features: (1) photogeneration of mid-gap spectral weight associated to parity-forbidden optical states, and (2) melting of the excitonic peak and emergence of a Fano-like optical resonance due to quantum interference of the excitons and the absorption band. The resulting nonequilibrium optical excitations correspond to renormalized excitons or unbound doublon-holon pairs, upon decreasing of intersite Coulomb repulsion, respectively. Our results have direct relevance to pump and probe spectroscopy experiments in the THz domain performed on organic salts such as ET-F$_2$TCNQ, where quantum interference between excitons and absorption-band states give rise to nonequilibrium optical excitations and photometallization.

Quantum materials with broken inversion symmetry carry a potential for novel quadratic optical responses, for instance, photovoltaic effect and second harmonic generations [1]. These nonlinear optical responses have attracted much attention in the aspect of an application for the next-generation optical-electronic devices, such as unconventional solar cells and optical sensors. However, previous studies on nonlinear optical responses mainly focused on systems of noninteracting electrons, and effects from strongly correlated systems have not been fully explored so far despite the possibility of enhanced and controlled responses through the multi-degree of freedom of electrons. In this study, we focus on noncentrosymmetric magnets as an example among a variety of strongly correlated materials. Based on the diagrammatic method [2], we theoretically investigate linear and nonlinear optical conductivities on the two types of one-dimensional noncentrosymmetric magnetic systems. First, we show the photovoltaic effect and second harmonic generation in electrons coupled to a chiral magnet with the Dzyaloshinskii-Moriya interaction. We find that these quadratic responses in the chiral magnets can be colossal and vary drastically depending on the frequency of the incident lights, the magnetization, and the spin-charge coupling [3]. Second, we also study the photovoltaic effect in a cycloidal magnet with alternating coupling constants. We find that such spin systems without spatial inversion symmetry support the shift current response through magnon excitations under the strong spin-charge coupling [4]. Since the present mechanisms do not require the spin-orbit coupling, which is small and usually suppresses the optical responses, such responses have the potential to exhibit large nonlinear functionality. [1] Y. Tokura and N. Nagaosa, Nat. Commun. {\bf 9}, 3740 (2018). [2] D. E. Parker, T. Morimoto, J. Orenstein, and J. E. Moore, Phys. Rev. B {\bf 99}, 045121 (2019). [3] S. Okumura, T. Moritomo, Y. Kato, and Y. Motome, Phys. Rev. B {\bf 104}, L180407 (2021). [4] T. Morimoto, S. Kitamura, and S. Okumura, Phys. Rev. B {\bf 104}, 075139 (2021).

The tripartite information is an observable-independent measure for scrambling and delocalization of information. It provides a new diagnostic for the dynamics of quantum many-body systems, which we employ to analyze various spin chain models. Specifically, it turns out to be a good observable-independent indicator for distinguishing between many-body localized and delocalized regimes. O. Schnaack, N. Boelter, S. Paeckel, S. Manmana, S. Kehrein, and M. Schmitt, Phys. Rev. B 100 (2019) 224302 N. Boelter and S. Kehrein, Phys. Rev. B 105 (2022) 104202

Driven quantum systems may realize novel phenomena absent in static systems, but driving-induced heating can limit the time-scale on which these persist. We study heating in interacting quantum many-body systems driven by random sequences with n−multipolar correlations, corresponding to a polynomially suppressed low frequency spectrum. For n≥1, we find a prethermal regime, the lifetime of which grows algebraically with the driving rate, with exponent 2n+1. We justify this scaling behaviour based on Fermi's golden rule [1] as well as generalized Floquet-Magnus expansion [2]. Despite the absence of periodicity in the drive, and in spite of its eventual heat death, the prethermal regime can host versatile non-equilibrium phases, which we illustrate with a random multipolar discrete time crystal [1] and anomalous random multipolar driven insulators [3]. References: 1. Phys. Rev. Lett. 126, 040601, 2. Phys. Rev. Lett. 127, 050602, 3. arXiv:2201.05406

We show the preservation of coarse-grained memory of the initial state for unexpectedly long times for density waves in a hardcore boson ring exchange model on a square lattice. Athough this is inconsistent with the prediction from a low frequency continuum theory, we find that the decay of the initial pattern is consistent with the predictions from the continuum theory. To further understand the mechanism leading to the long time preservation and eventual melt of the stripe like initial condition, we present detailed correlation functions of the dynamically active regions and find the formation of unconventional long range patterns, which control the melting process.

Periodically driven quantum systems suffer from heating via resonant excitation. While such Floquet heating guides a generic isolated system towards the infinite temperature state, a driven open system, coupled to a thermal bath, will approach a non-equilibrium steady state, which is determined by the interplay of driving and dissipation. Here, we show that this interplay can give rise to the counterintuitive effect that Floquet heating can induce Bose condensation. We consider a one-dimensional Bose gas in an optical lattice of finite extent, which is coupled weakly to a three-dimensional thermal bath given by a second atomic species. The bath temperature T lies well above the crossover temperature, below which the majority of the system's particles form a (finite-size) Bose condensate in the ground state. However, when a strong local potential modulation is switched on, which resonantly excites the system, a non-equilibrium Bose condensate is formed in a state that decouples from the drive. Our predictions, which are based on a microscopic model that is solved using kinetic equations of motion derived from Floquet-Born-Markov theory, can be probed under realistic experimental conditions.

The wildly growing field researching optically-induced ultrafast coherent spin dynamics in solids mainly relies on the direct excitation of magnon modes via either resonant pumping[1-2] or non-resonant impulsive stimulated Raman scattering[3-4]. The latter has been widely demonstrated to be effective even at the edges of the Brillouin zone[5-6] and in the absence of laser-heating of electrons and the lattice[7]. Typically the photo-generation of magnon modes and the subsequent spin dynamics are investigated in single-domain states, i.e. the laser beams are focused into a single domain. Multi-domain states, occurring for instance in the ground state of antiferromagnets, are perceived as a nuisance to be avoided for an efficient control of spins. In my talk I will discuss recent results, which experimentally disprove this commonly accepted wisdom. Relying on a spectroscopic opto-magnetic investigation of the femtosecond spin dynamics in the archetypal antiferromagnet NiO in a multi-domain state I will discuss: i) the excitation and a novel mechanism to arbitrary amplify a THz magnon mode, which relies on electronic-spin correlations, i.e. via the exciton-magnon transition[8]; ii) nonlinear femtosecond spin dynamics, in the form of coupling between the different magnon modes, typically orthogonal in a single- domain state; iii) the microscopic nature of the coupling between modes, which is due to the presence of domain walls. This last point was supported by a phenomenological model[9] and, most importantly, by means of a control experiment performed in a single domain of the material. This experiment confirms that the coupling between the modes requires domain walls, as it is not observed in a single domain[10]. [1] Nature Photonics 5, 31–34 (2010). [2] Physical Review Letters 117, 197201 (2016). [3] Nature 435, 655–657 (2005). [4] Reviews of Modern Physics 82, 2731–2784 (2010). [5] Nature Communications 7, 10645 (2016). [6] Physical Review B 100, 024428 (2019). [7] Physical Review B 89, 060405–060405 (2014). [8] Nature Physics14, 370 (2018) [9] J. Phys. D: Appl. Phys. 54, 374004 (2021) [10] Physical Review Letters 127, 077202 (2021)

Using ultrashort laser pulses, it has become possible to probe the dynamics of long-range order in solids on microscopic timescales. In the conventional description of symmetry-broken phases within time-dependent Ginzburg-Landau theory, the order parameter evolves coherently along an average trajectory. Recent experiments, however, indicate the profound effect of order parameter fluctuations on the dynamics. An extreme scenario is ultrafast inhomogeneous disordering, where the average order parameter is no longer representative of the state on the atomic scale. While this has a profound effect on the dynamics, a theoretical approach which takes into account atomic scale inhomogeneities of both the electronic structure and the order parameter is challenging. In my talk, I will report on results for the Holstein model, which are based on a nonequilibrium generalization of statistical dynamical mean-field theory, coupled to stochastic differential equations for the order parameter [1]. The results show that ultrafast disordering can occur already in this minimal model for the Peierls charge-density wave transition. Similar techniques may help in future to solve the coupled electron lattice dynamics for strongly interacting electrons. [1] Antonio Picano, Francesco Grandi, Martin Eckstein, arXiv:2112.15323.

In this talk I will discuss recent progress in controlling and inducing materials properties with light [1]. Specifically I will discuss recent experiments showing light-induced superconductivity through phonon driving in an organic kappa salt [2] and its possible theoretical explanation via dynamical Hubbard U [3]. I will then highlight some recent theoretical and experimental progress in cavity quantum materials [4], where the classical laser as a driving field of light-induced properties is replaced by quantum fluctuations of light in confined geometries. Ideas and open questions for future work will be outlined. [1] Colloquium: Nonthermal pathways to ultrafast control in quantum materials, A. de la Torre, D. M. Kennes, M. Claassen, S. Gerber, J. W. McIver, M. A. Sentef, Rev. Mod. Phys. 93, 041002 (2021). [2] Photo-molecular high temperature superconductivity, M. Buzzi, D. Nicoletti, M. Fechner, N. Tancogne-Dejean, M. A. Sentef, A. Georges, M. Dressel, A. Henderson, T. Siegrist, J. A. Schlueter, K. Miyagawa, K. Kanoda, M.-S. Nam, A. Ardavan, J. Coulthard, J. Tindall, F. Schlawin, D. Jaksch, A. Cavalleri, Phys. Rev. X 10, 031028 (2020). [3] Dynamical Superconductivity in a Frustrated Many-Body System, J. Tindall, F. Schlawin, M. Buzzi, D. Nicoletti, J. R. Coulthard, H. Gao, A. Cavalleri, M. A. Sentef, D. Jaksch, Phys. Rev. Lett. 125, 137001 (2020). [4] Cavity Quantum Materials,
Frank Schlawin, Dante M. Kennes, Michael A. Sentef,
 Applied Physics Reviews Reviews 9, 011312 (2022).
[OA] arXiv:2112.15018

Engineering the collective behaviour of particles in quantum materials is considered a new paradigm in material design. One enticing possibility is to create collective light-matter-hybrid states by embedding materials inside optical cavities [1, 2]. In an optical cavity, the confinement of light on a small region of space can result in strong light-matter coupling and hence alter the properties of the material altogether. Here I demonstrate, based on first principles calculations, that the strong light-matter coupling in a cavity can induce a change of the collective phase from paraelectric to ferroelectric in the groundstate of SrTiO3 [3], which has thus far only been achieved in out-of-equilibrium strongly excited conditions [5, 6]. This is a light-matter-hybrid groundstate which can only exist because of the coupling to the vacuum fluctuations of light, a photo-groundstate. The atomistic calculations show the nuclear quantum fluctations of the SrTiO3 lattice, the ones responsible for the quantum paraelectricity of the SrTiO3 [7], can be suppressed by means of the coupling to the vacuum fluctuations of light in a process that is analogous to dynamical localisation: the interaction with cavity photons results in an enhancement of the effective mass of the ions thus slowing them down and reducing the strength of their quantum fluctuations. I further demonstrate that the effect of cavity induced localization extends to finite temperatures, even when thermal lattice fluctuations overcome the quantum ones. I thus introduce a revisited paraelectric to ferroelectric phase diagram, with the cavity coupling strength as new dimension. These findings ultimately demonstrate how exposing a material to confined light can change fundamental properties of its groundstate as far as its crystal structure. [1] H. Huebener, et al., Nature Materials 13, 1045 (2020). [2] M. Ruggenthaler, N. Tancogne-Dejean, J. Flick, H. Appel, A. Rubio, Nature Reviews Chemistry 2, 1 (2018). [3] S. Latini, D. Shin, S. A Sato, C. Schäfer, U. De Giovannini, H. Hübener, & A. Rubio (2021). Proceedings of the National Academy of Sciences, 118(31). [5] X. Li, et al., Science 364, 1079 (2019). [6] T. F. Nova, A. S. Disa, M. Fechner, A. Cavalleri, Science 364, 1075 (2019). [7] D. Shin, S. Latini, S. A Sato, C. Schäfer, U. De Giovannini, H. Hübener, & . Rubio Physical Review B, 104(6), L060103.

Floquet engineering has become a growing paradigm of nonequilibrium phenomena in condensed matter system. One fascinating aspect of the Floquet engineering is that it can realize novel quantum phases inaccessible in equilibrium. Striking example are the light-induced chiral gauge field in Dirac electron systems and emergence of new topological phases such as Floquet-Weyl states. In this talk, we report on the light-induced anomalous Hall effect(AHE) in three dimensional Dirac electron systems probed by time-resolved terahertz Faraday effect. The possible origin of the observed AHE will be discussed in terms of the chiral gauge field.

The responses of materials to high intensity light, i.e., nonlinear optical responses, constitute a vast field of physics and engineering. One of nonlinear optical responses that are attracting a recent keen attention is a bulk photovoltaic effect called shift current which arises from a geometrical (Berry) phase of a Bloch wave function and has a close relationship to the modern theory of electric polarization [1]. While most previous studies of the bulk photovoltaic effects have focused on band insulators of noninteracting electrons, systems of correlated electrons have a potential to support a novel nonlinear functionality. In this talk, I will present our recent efforts in seeking nonlinear optical effects originating from unique excitations in interacting electron systems, including excitons in semiconductors [2], magnetic excitations in multiferroic materials [3], and phonon excitations in electron-phonon coupled systems [4], where excitations below the electronic band gap generate novel photovoltaic effects through the shift current mechanism. [1] T. Morimoto, and N. Nagaosa, Sci. Adv. 2, e1501524 (2016). [2] T. Morimoto, and N. Nagaosa, Phys. Rev. B 94, 035117 (2016). [3] T. Morimoto, S. Kitamura, S. Okumura, Phys. Rev. B 104, 075139 (2021). [4] Y. Okamura et al. PNAS 119, e2122313119 (2022).

The selfconsistent theoretical treatment of correlation and quantum effects in nonequilibrium beyond one-dimensional systems is a particular challenge that has been successfully attacked with nonequilibrium Green functions (NEGF) methods [1]. However, NEGF simulations are hampered by a cubic scaling of the computation time with the number of time steps $N_t$. Recently, a dramatic acceleration has been achieved within the G1–G2 scheme [2] by transforming the NEGF equations, within the Hartree-Fock Generalized Kadanoff–Baym ansatz (GKBA) [3], to a time-local form for the single-particle and two-particle Green functions. A detailed discussion of the method and its application to a variety of selfenergies including particle-particle and particle-hole $T$ matrix, $GW$, and the dynamically screened ladder (DSL) was presented recently [4]. Due to its relation to the single-time BBGKY hierarchy, the G1–G2 scheme can benefit from a variety of well-established techniques of two-particle reduced density matrix (2RDM) theory, such as enforcing contraction consistency or a purification of the dynamics, to further improve its accuracy and numerical stability [5]. A drawback of the G1–G2 scheme is the memory cost needed to store the two-particle Green function. This can be significantly relieved by using a recently developed alternative stochastic approach to the G1–G2 scheme [6]. We present first results for the stochastic $GW$ approximation. [1] N. Schlünzen et al., PRB 93, 035107 (2016) [2] N. Schlünzen et al., PRL 124, 076601 (2020) [3] P. Lipavský, V. Špička, and B. Velický, PRB 34, 6933 (1986) [4] J.-P. Joost et al., PRB 101, 245101 (2020) [5] J.-P. Joost et al., PRB 105, 165155 (2022) [6] E. Schroedter et al., submitted to Cond. Matt. Phys. (2022), arXiv:2204.08250

This talk will focus on the time-integration of the `three-contour' Baym Kadanoff equations and the calculation of second-order self-energies. Special emphasis is placed on obtaining results for multi-orbital systems such as molecules with realistic Coulomb interactions, as well as couplings to a light field and single-particle excitation spectra. We will examine the performance of numerical techniques such as efficient basis functions and adaptive compression schemes. Comparisons to real frequency spectra obtained with equilibrium methods and Nevanlinna continuation are shown.

Observing signatures of light-induced Floquet topological states in materials has been shown to be very challenging. Angle-resolved photoemission spectroscopy (ARPES) is well suited for the investigation of Floquet physics, as it allows to directly probe the dressed electronic states of driven solids. Depending on the system, scattering and decoherence can play an important role, which has hampered the observation of Floquet states. Another challenge is to disentangle Floquet side bands from laser-assisted photoemission (LAPE), since both lead to similar signatures in ARPES spectra. In this talk, we will discuss how to tackle these challenges with advances in time-resolved ARPES (trARPES). First, we investigate the emergence of Floquet state in the transition metal dichalcogenide 2H-WSe$_2$, one of the most promising systems for observing Floquet physics. Based on fully ab initio treatment of the light-matter interaction, we discuss how the Floquet topological state manifests in characteristic features in the circular dichroism in photoelectron angular distributions. Combining highly accurate modeling of the photoemission matrix elements with an ab initio description of the light-matter interaction, we investigate regimes which can be realized in current state-of-the-art experimental setups. We also discuss the ultrafast “birth” of Floquet-Bloch bands from the topological surface state of Bi$_2$Te$_3$ probed by subcycle trARPES. The combination of experiment and theory paves the way for realizing Floquet states down to the ultimate few-cycle limit.

We propose a three-step periodic drive protocol to engineer two-dimensional~(2D) Floquet quadrupole superconductors and three-dimensional~(3D) Floquet octupole superconductors hosting zero-dimensional Majorana corner modes~(MCMs), based on unconventional $d$-wave superconductivity. Remarkably, the driven system conceives four phases with only 0 MCMs, no MCMs, only anomalous $\pi$ MCMs, and both regular 0 and anomalous $\pi$ MCMs. To circumvent the subtle issue of characterizing 0 and $\pi$ MCMs separately, we employ the periodized evolution operator to architect the dynamical invariants, namely quadrupole and octupole motion in 2D and 3D, respectively, that can distinguish different higher-order topological phases unambiguously. Our study paves the way for the realization of dynamical quadrupolar and octupolar topological superconductors. Ref: Phys. Rev. B 105, 155406 (2022)

Interference in quantum dynamics cannot be delayed beyond an Ehrenfest time scale, which therefore delimits the quantum-classical correspondence. Nevertheless, for bosonic many-body quantum systems with a mean-field limit, advanced semiclassical methods do incorporate genuine many-body quantum interferences accurately for large particle numbers relying exclusively on such mean-field solutions. In this way, system specific non-equilibrium quantum dynamical features, which cannot be captured in detail within a truncated Wigner approximation, can still be understood with the knowledge of mean field solutions. We illustrate the predictive power of pre- and post-Ehrenfest semiclassical dynamics with the example of coherent state propagation in a Bose-Hubbard model.

The interaction of photons with molecules or atoms coupled to vibrations are often described by Jaynes-Cummings or spin-boson models. Commonly, these models are treated via a rate-equation approach [1] due to the non-canonical dynamics of the (spin-like) electronic excitations. However, this approach does not account for non-Markovian dynamics of the internal vibrational states. We introduce a novel auxilliary-particle formulation for the electronic and vibrational state of the molecules. This field-theoretical approach can be applied in and out of equilibrium and can capture non-Markovian dynamics, large reservoir sizes as well as spontaneously broken U(1) symmetry due to Bose-Einstein condensation. We present results for a pump cavity system filled with a dilute dye solution showing a BEC transition of photons [2]. Further generalisations of this formulation can be applied to various open or closed multi-level systems. [1] P. Kirton, J. Keeling, Phys. Rev. Lett. 111, 100404 (2013). [2] J. Klaers, J. Schmitt, F. Vewinger, M. Weitz, Nature 468, 545 (2010).

We describe coupled electron-phonon systems semiclassically—Ehrenfest dynamics for the phonons and quantum mechanics for the electrons—using a classical Monte Carlo approach that determines the nonequilibrium response to a large pump field. The semiclassical approach is quite accurate, because the phonons are excited to average energies much higher than the phonon frequency, eliminating the need for a quantum description. The numerical efficiency of this method allows us to perform a self-consistent time evolution out to very long times (tens of picoseconds) enabling us to model pump-probe experiments of a charge density wave (CDW) material. Our system is a half-filled, one-dimensional (1D) Holstein chain that exhibits CDW ordering due to a Peierls transition. The chain is subjected to a time-dependent electromagnetic pump field that excites it out of equilibrium, and then a second probe pulse is applied after a time delay. By evolving the system to long times, we capture the complete process of lattice excitation and subsequent relaxation to a new equilibrium, due to an exchange of energy between the electrons and the lattice, leading to lattice relaxation at finite temperatures. We employ an indirect (impulsive) driving mechanism of the lattice by the pump pulse due to the driving of the electrons by the pump field. We identify two driving regimes, where the pump can either cause small perturbations or completely invert the initial CDW order. Our work successfully describes the ringing of the amplitude mode in CDW systems that has long been seen in experiment.

We benchmark a set of quantum-chemistry methods including the multitrajectory Ehrenfest, the fewest-switches surface-hopping, and the multiconfigurational Ehrenfest method against exact quantum-many-body techniques by studying real-time dynamics in the Holstein model up to 51 sites. We address both the physics of single Holstein polarons and the dynamics of charge-density waves at finite electron densities. For larger systems, we compare the quantum-chemistry methods to exact dynamics obtained from time-dependent density matrix renormalization group calculations with local basis optimization (DMRG-LBO). Our results show that the multitrajectory Ehrenfest method in general only captures the ultra-short time dynamics accurately and that the surface-hopping method with suitable corrections provides a much better description of the long-time behavior. We further show that the multiconfigurational Ehrenfest method yields a significant improvement over the multitrajectory Ehrenfest method and can be converged to the exact results in small systems with moderate computational efforts, however, for extended systems, this convergence is slower with respect to the number of configurations. Our benchmark study demonstrates that DMRG-LBO is a useful tool for assessing the quality of the quantum-chemistry methods.

We compute the optical conductivity for the Holstein polaron and bipolaron with dispersive phonons at finite temperature using a matrix-product state-based method. We combine purification [1], to obtain the finite-temperature states [2], together with the parallel time-dependent variational principle (pTDVP) [3] algorithm to compute the real-time current-current correlation functions. The pTDVP algorithm utilizes local basis optimization [4] to efficiently treat the phononic degrees of freedom. For the polaron, we find that the phonon dispersion alters the optical conductivity at several temperatures in the weak, intermediate, and strong coupling regimes. In the two first cases, we see that the spectrum goes from being continuous to discrete when going from an upwards to a downwards phonon dispersion relation. In the strong coupling regime, the dispersion leads to a shift of the center of the spectrum. For the bipolaron, we also see that the dispersion shifts the spectrum. The results fit well with an analytical expression derived from the Born-Oppenheimer Hamiltonian. [1] Verstraete et al., Phys. Rev. Lett. 93, 207204 (2004) [2] Jansen et al., Phys. Rev. B 102, 165155 (2020) [3] Secular et al., Phys. Rev. B 101, 235123 (2020) [4] Zhang et al., Phys. Rev. Lett. 80, 2661 (1998)

We developed a new formalism to study non-equilibrium dynamics of scalar fields using Keldysh field theory. We use our formalism to study non-equilibrium dynamics of phonons coupled to thermal baths. When connected to an Ohmic bath, all phonon modes thermalize as expected. On the other hand when we couple the phonons to one-dimensional fermionic bath, low wavelength modes fail to thermalize at all temperatures. At low temperatures, constraints from energy-momentum conservation lead to a narrow bandwidth of particle-hole excitations and the phonons effectively do not see this bath. On the other hand, the strong band edge divergence of particle-hole density of states leads to an undamped "polariton-like" mode of the dressed phonons above the band edge of the particle-hole excitations. These undamped modes contribute to the lack of thermalization of long wavelength phonons at high temperatures. In higher dimensions, these constraints and the divergence of density of states are weakened and leads to thermalization at all wavelengths.

Transition metal dichalcogenides (TMDs) are an exciting model system to study ultrafast energy dissipation pathways, and to create and tailor new emergent quantum phases [1,2]. The versatility of TMDs results from the confinement of optical excitations in two-dimensions and the concomitant strong Coulomb interaction that leads to excitonic quasiparticles with binding energies in the range of several 100 meV. In TMD stacks consisting of at least two layers, the interlayer interaction can be precisely controlled by manipulating the twist angle: The misalignment of the crystallographic directions leads to a momentum mismatch between the high symmetry points of the hexagonal Brillouin zones. This strongly impacts the interlayer wavefunction hybridization, and, moreover, adds an additional moiré potential. Crucially, in this emergent energy landscape, dark intra- and interlayer excitons dominate the energy dissipation pathways. While these dark excitonic features are hard to access in all-optical experiments, time-resolved momentum microscopy [3] can provide unprecedented insight on these quasiparticles [4]. In my talk, I will present our recent results on the ultrafast formation dynamics of interlayer excitons in twisted WSe$_2$/MoS$_2$ heterostructures. First, I will report on the identification of a hallmark signature of the moiré superlattice that is imprinted onto the momentum-resolved interlayer exciton photoemission signal. With this data, we reconstruct the electronic part of the exciton wavefunction, and relate its extension to the moiré wavelength of the heterostructure. Second, I will show that interlayer excitons are effectively formed via exciton-phonon scattering, and subsequent interlayer tunneling at the interlayer hybridized $\Sigma$ valleys on the sub-50 fs timescale. Finally, I will discuss our recent efforts to monitor the interlayer exciton formation dynamics with spatiotemporal resolution using femtosecond photoelectron dark-field microscopy. References [1] Wang et al., Rev. Mod. Phys. 90, 021001 (2018). [2] Wilson et al., Nature 599, 383 (2021). [3] Keunecke et al., Rev. Sci. Ins. 91, 063905 (2020). [4] Schmitt et al., arXiv:2112.05011(2021).

Random quantum circuits provide a useful lens on the universal features of quantum dynamics far from equilibrium. Such circuits are particularly attractive in the context of noisy intermediate-scale quantum (NISQ) devices, where they found applications for instance to achieve a quantum computational advantage and to explore quantum information scrambling. In this talk, we discuss that random quantum circuits are tailor-made building blocks for simulating quantum many-body dynamics on NISQ devices. Relying on the concept of quantum typicality, we propose an algorithm to study quantum hydrodynamics based on the buildup of spatiotemporal correlation functions in one- and two-dimensional quantum spin systems. We particularly scrutinize the inevitable impact of errors present in any realistic implementation. Furthermore, we introduce a class of long-range random Clifford circuits with U(1) symmetry, where the emerging transport behavior varies depending on the exponent which controls the probability of gates spanning a certain range. Given their efficient classical simulability even for large system sizes, such circuits provide an ideal framework to study the slowdown of higher Renyi entropies in quantum systems with conservation laws. Specifically, we demonstrate that the different hydrodynamic regimes are directly reflected in the asymptotic entanglement growth, which we explain in terms of the inhibited operator spreading in U(1)-symmetric Clifford circuits, where the emerging light cones are intimately related to the transport behavior. Our work highlights the practical relevance of random circuits in the NISQ era and their versatility to explore questions in nonequilibrium many-body quantum systems. [1] J. Richter and A. Pal, Phys. Rev. Lett. 126, 230501 (2021). [2] O. Lunt, J. Richter, and A. Pal, arXiv:2112.06682. [3] J. Richter, O. Lunt, and A. Pal, arXiv:2205.06309.

A central topic in current research in non-equilibrium physics is the design of pathways to control and induce order in correlated electron materials with time-dependent electromagnetic fields. The theoretical description of such processes, in particular in two spatial dimensions, is very challenging and often relies on phenomenological modelling in terms of free energy landscapes. In this talk I will present a semiclassical time evolution scheme that includes dephasing dynamics beyond mean-field and allows to simulate the light-induced manipulation of prethermal order in a two-dimensional model with competing phases microscopically. I will discuss the time evolution of the relevant order parameters subsequent to driving with a short laser pulse. The induced prethermal order does not depend on the amount of absorbed energy alone but also explicitly on the driving frequency and amplitude. While this dependency is pronounced in the low-frequency regime, it is suppressed at high driving frequencies. arXiv:2205.06620 (A. Osterkorn, S. Kehrein)

I will discuss the dissipative dynamics of a periodically driven inhomogeneous critical lattice model in one dimension. The closed system dynamics starting from pure initial states is well-described by a driven Conformal Field Theory (CFT), which predicts the existence of both heating and non-heating phases in such systems. Heating is inhomogeneous and is manifested via the emergence of black-hole like horizons in the system. Based on exact calculations of the time evolution of the lattice density matrix, I will demonstrate that for short and intermediate times, the closed system phase diagram comprising heating and non-heating phases, persists for thermal initial states on the lattice. Secondly, in the fully open system with boundary dissipators, I will show that the nontrivial spatial structure of the heating phase survives particle-conserving and non-conserving dissipations through clear signatures in mutual information and energy density evolution.

Several mechanisms have been identified that can lead to a breakdown of thermalization in closed quantum systems—including integrability and many-body localization. Recently, a novel mechanism has been discovered in systems where the Hilbert space fragments into exponentially many disconnected sectors due to constrained dynamics. First, we show how local constraints yield an extensive fragmentation of the Hilbert space, which in turn can lead to a breakdown of thermalization of closed quantum systems. Second, we demonstrate that the non-thermal behavior can persist even when the fragmented system is coupled to a dissipative bath as long as the Liouvillian preserves certain symmetries.