Nonequilibrium Dynamical Mean-field Theory Research Articles

Configuration interaction based nonequilibrium steady state impurity solver

We present a solver for correlated impurity problems out of equilibrium based on a combination of the so-called auxiliary master equation approach (AMEA) and the configuration interaction expansion. Within AMEA one maps the original impurity model onto an auxiliary open quantum system with a restricted number of bath sites which can be addressed by numerical many-body approaches such as Lanczos/Arnoldi exact diagonalization (ED) or matrix product states (MPS). While the mapping becomes exponentially more accurate with increasing number of bath sites, ED implementations are severely limited due to the fast increase of the Hilbert space dimension for open systems, and the MPS solver typically requires rather long runtimes. Here, we propose to adopt a configuration interaction approach augmented by active space extension to solve numerically the correlated auxiliary open quantum system. This allows access to a larger number of bath sites at lower computational costs than for plain ED. We benchmark the approach with numerical renormalization group results in equilibrium and with MPS out of equilibrium. In particular, we evaluate the current, the conductance, as well as the Kondo peak and its splitting as a function of increasing bias voltage below the Kondo temperature ${T}_{\text{K}}$. We obtain a rather accurate scaling of the conductance as a function of the bias voltage and temperature rescaled by ${T}_{\text{K}}$ for moderate to strong interactions in a wide range of parameters. The approach combines the fast runtime of ED with an accuracy close to the one achieved by MPS making it an attractive solver for nonequilibrium dynamical mean field theory.

Impact ionization processes in a photodriven Mott insulator: Influence of phononic dissipation

We study a model for photovoltaic energy collection consisting of a Mott insulating layer in presence of acoustic phonons, coupled to two wide-band fermion leads at different chemical potentials and driven into a nonequilibrium steady state by a periodic electric field. We treat electron correlations with nonequilibrium dynamical mean-field theory (DMFT) using the so-called auxiliary master equation approach as impurity solver and include dissipation by acoustic phonons via the Migdal approximation. For a small hybridization to the leads, we obtain a peak in the photocurrent as a function of the driving frequency which can be associated with impact ionization processes. For larger hybridizations the shallow peak suggests a suppression of impact ionization with respect to direct photovoltaic excitations. Acoustic phonons slightly enhance the photocurrent for small driving frequencies and suppress it at frequencies around the main peak at all considered hybridization strengths.

Local interpretation of time-resolved x-ray absorption in Mott insulators: Insights from nonequilibrium dynamical mean-field theory

We present a formalism based on nonequilibrium dynamical mean field theory (DMFT) which allows to compute the time-resolved X-ray absorption spectrum (XAS) of photo-excited solids. By applying this formalism to the photo-doped half-filled and quarter-filled two-orbital Hubbard models in the Mott insulating regime we clarify how the time-resolved XAS signal reflects the nonequilibrium population of different local states. Apart from the missing broadening associated with continuum excitations, the atomic XAS spectrum computed with the nonthermal state populations provides a good approximation to the full nonequilibrium DMFT result. This suggest a route to combine the accurate DMFT description of nonequilibrum states of solids with cluster calculations of the XAS signal.

Correlated Mott insulators in strong electric fields: Role of phonons in heat dissipation

We study the spectral and transport properties of a Mott insulator driven by a static electric field into a non-equilibrium steady state. For the dissipation, we consider two mechanisms: Wide-band fermion reservoirs and phonons included within the Migdal approximation. The electron correlations are treated via non-equilibrium dynamical mean field theory with an impurity solver suitable for strong correlations. We find that dissipation via phonons is limited to restricted ranges of field values around Wannier-Stark resonances. To cover the full range of field strengths, we allow for a small coupling with fermionic baths, which stabilizes the solution. When considering both dissipation mechanisms, we find that phonons enhance the current for field strengths close to half of the gap while lowering it at the gap resonance as compared to the purely electronic dissipation used by Murakami and Werner [arXiv:1804.08257]. Once phonons are the only dissipation mechanism, the current in the metallic phase is almost one order of magnitude smaller than the typical values obtained by coupling to a fermionic bath. In this case, the transport regime is characterized by an accumulation of charge in the upper Hubbard band described by two effective chemical potentials.

Nonadiabatic Exchange-Correlation Potential for Strongly Correlated Materials in the Weak and Strong Interaction Limits

In this work, nonadiabatic exchange-correlation (XC) potentials for time-dependent density-functional theory (TDDFT) for strongly correlated materials are derived in the limits of strong and weak correlations. After summarizing some essentials of the available dynamical mean-field theory (DMFT) XC potentials valid for these systems, we present details of the Sham–Schluter equation approach that we use to obtain, in principle, an exact XC potential from a many-body theory solution for the nonequilibrium electron self-energy. We derive the XC potentials for the one-band Hubbard model in the limits of weak and strong on-site Coulomb repulsion. To test the accuracy of the obtained potentials, we compare the TDDFT results obtained with these potentials with the corresponding nonequilibrium DMFT solution for the one-band Hubbard model and find that the agreement between the solutions is rather good. We also discuss possible directions to obtain a universal XC potential that would be appropriate for the case of intermediate interaction strengths, i.e., a nonadiabatic potential that can be used to perform TDDFT analysis of nonequilibrium phenomena, such as transport and other ultrafast properties of materials with any strength of electron correlation at any value in the applied perturbing field.

Nonequilibrium resonant inelastic x-ray scattering study of an electron-phonon model

We use the nonequilibrium dynamical mean field theory formalism to compute the equilibrium and nonequilibrium resonant inelastic X-ray scattering (RIXS) signal of a strongly interacting fermionic lattice model with a coupling of dispersionless phonons to the total charge on a given site. In the atomic limit, this model produces phonon subbands in the spectral function, but not in the RIXS signal. Electron hopping processes however result in phonon-related modifications of the charge excitation peak. We discuss the equilibrium RIXS spectra and the characteristic features of nonequilibrium states induced by photo-doping and by the application of a static electric field. The latter produces features related to Wannier-Stark states, which are dressed with phonon sidebands. Thanks to the effect of field-induced localization, the phonon features can be clearly resolved even in systems with weak electron-phonon coupling.

Quantum Boltzmann equation for strongly correlated electrons

Collective orders and photoinduced phase transitions in quantum matter can evolve on timescales which are orders of magnitude slower than the femtosecond processes related to electronic motion in the solid. Quantum Boltzmann equations can potentially resolve this separation of timescales, but are often constructed by assuming the existence of quasiparticles. Here we derive a quantum Boltzmann equation which only assumes a separation of timescales (taken into account through the gradient approximation for convolutions in time), but is based on a nonperturbative scattering integral, and makes no assumption on the spectral function such as the quasiparticle approximation. In particular, a scattering integral corresponding to nonequilibrium dynamical mean-field theory is evaluated in terms of an Anderson impurity model in a nonequilibrium steady state with prescribed distribution functions. This opens the possibility to investigate dynamical processes in correlated solids with quantum impurity solvers designed for the study of nonequilibrium steady states.

Accelerated gap collapse in a Slater antiferromagnet

We study the melting of long-range antiferromagnetic order in the Hubbard model after an interaction quench, using non-equilibrium dynamical mean-field theory. From previous studies, the system is known to quickly relax into a prethermal symmetry-broken state. Using a convergent truncation of the memory integrals in the Kadanoff Baym equations, we unravel the subsequent relaxation dynamics of this state over several orders of magnitude in time. At long times, the prethermal state can be characterized by a single slow variable which is related to the conduction band population. The dynamics of this variable does not follow the paradigmatic steady relaxation of pre-thermal states: It is highly nonlinear, with a pronounced speedup once the gap falls below a certain value. This behavior indicates that non-thermal order can be self-stabilized on some timescale. It is not reproduced using simple Fermi's golden rule estimate for the evolution of the conduction band population.

Simulation of time-dependent resonant inelastic x-ray scattering using nonequilibrium dynamical mean-field theory

We develop a framework to evaluate the time-dependent resonant inelastic X-ray scattering (RIXS) signal with the use of non-equilibrium dynamical mean field theory simulations. The approach is based on the solution of a time-dependent impurity model which explicitly incorporates the probe pulse. It avoids the need to compute four-point correlation functions, and can in principle be combined with different impurity solvers. This opens a path to study time-resolved RIXS processes in multi-orbital systems. The approach is exemplified with a study of the RIXS signal of a melting Mott antiferromagnet.

Nonequilibrium-DMFT based RIXS investigation of the two-orbital Hubbard model

Resonant inelastic X-ray scattering (RIXS) detects various types of high- and low-energy elementary excitations in correlated solids, and this tool will play an increasingly important role in investigations of time-dependent phenomena in photo-excited systems. While theoretical frameworks for the computation of equilibrium RIXS spectra are well established, the development of appropriate methods for nonequilibrium simulations is an active research field. Here, we apply a recently developed nonequilibrium dynamical mean field theory (DMFT) based approach to compute the RIXS response of photo-excited two-orbital Mott insulators. The results demonstrate the feasibility of multi-orbital nonequilibrium RIXS calculations and the sensitivity of the quasi-elastic fluorescence-like features and excitation peaks on the nonequilibrium population of the Hubbard bands.

Ultrafast Mott transition driven by nonlinear electron-phonon interaction

Nonlinear phononics holds the promise for controlling properties of quantum materials on the ultrashort timescale. Using nonequilibrium dynamical mean-field theory, we solve a model for the description of organic solids, where correlated electrons couple nonlinearly to a quantum phonon mode. Unlike previous works, we exactly diagonalize the local phonon mode within the noncrossing approximation to include the full phononic fluctuations. By exciting the local phonon in a broad range of frequencies near resonance with an ultrashort pulse, we show it is possible to induce a Mott insulator-to-metal phase transition. Conventional semiclassical and mean-field calculations, where the electron-phonon interaction decouples, underestimate the onset of the quasiparticle peak. This fact, together with the nonthermal character of the photoinduced metal, suggests a leading role of the phononic fluctuations and of the dynamic nature of the state in the vibrationally induced quasiparticle coherence.

Dynamically induced doublon repulsion in the Fermi-Hubbard model probed by a single-particle density of states

We investigate the possibility to control dynamically the interactions between repulsively bound pairs of fermions (doublons) in correlated systems with off-resonant ac fields. We introduce an effective Hamiltonian that describes the physics of doublons up to the second-order in the high-frequency limit. It unveils that the doublon interaction, which is attractive in equilibrium, can be completely suppressed and then switched to repulsive by varying the power of the ac field. We show that the signature of the dynamical repulsion between doublons can be found in the single-fermion density of states averaged in time. Our results are further supported by nonequilibrium dynamical mean-field theory simulations for the half-filled Fermi-Hubbard model.

Characterizing the Non-equilibrium Dynamics of Field-Driven Correlated Quantum Systems

Recent experimental advances in ultrafast phenomena have triggered renewed interest in the dynamics of correlated quantum systems away from equilibrium. We review nonequilibrium dynamical mean-field theory studies of both the transient and the steady states of a DC field-driven correlated quantum system. In particular, we focus on the nonequilibrium behavior and how it relates to the fluctuation-dissipation theorem. The fluctuation-dissipation theorem emerges as an indicator for how the system thermalizes and for how it reaches a steady state. When the system thermalizes in an infinite temperature steady state it can pass through a succession of quasi-thermal states that approximately obey the fluctuation-dissipation theorem. We also discuss the Wigner distribution and what its evolution tells us about the nonequilibrium many-body problem.

NESSi: The Non-Equilibrium Systems Simulation package

The nonequilibrium dynamics of correlated many-particle systems is of interest in connection with pump–probe experiments on molecular systems and solids, as well as theoretical investigations of transport properties and relaxation processes. Nonequilibrium Green’s functions are a powerful tool to study interaction effects in quantum many-particle systems out of equilibrium, and to extract physically relevant information for the interpretation of experiments. We present the open-source software package NESSi (The Non-Equilibrium Systems Simulation package) which allows to perform many-body dynamics simulations based on Green’s functions on the L-shaped Kadanoff–Baym contour. NESSi contains the library libcntr which implements tools for basic operations on these nonequilibrium Green’s functions, for constructing Feynman diagrams, and for the solution of integral and integro-differential equations involving contour Green’s functions. The library employs a discretization of the Kadanoff–Baym contour into time N points and a high-order implementation of integration routines. The total integrated error scales up to O(N−7), which is important since the numerical effort increases at least cubically with the simulation time. A distributed-memory parallelization over reciprocal space allows large-scale simulations of lattice systems. We provide a collection of example programs ranging from dynamics in simple two-level systems to problems relevant in contemporary condensed matter physics, including Hubbard clusters and Hubbard or Holstein lattice models. The libcntr library is the basis of a follow-up software package for nonequilibrium dynamical mean-field theory calculations based on strong-coupling perturbative impurity solvers. Program summaryProgram Title: NESSiCPC Library link to program files:http://dx.doi.org/10.17632/973crf9hgd.1Licensing provisions: MPL v2.0Programming language: C++, pythonExternal routines/libraries: cmake, eigen3, hdf5 (optional), mpi (optional), omp (optional)Nature of problem: Solves equations of motion of time-dependent Green’s functions on the Kadanoff–Baym contour.Solution method: Higher-order solution methods of integral and integro-differential equations on the Kadanoff–Baym contour.

Light-induced evaporative cooling of holes in the Hubbard model

An elusive goal in the field of driven quantum matter is the induction of long-range order. Here, we propose a mechanism based on light-induced evaporative cooling of holes in a correlated fermionic system. Since the entropy of a filled narrow band grows rapidly with hole doping, the isentropic transfer of holes from a doped Mott insulator to such a band results in a drop of temperature. Strongly correlated Fermi liquids and symmetry-broken states could thus be produced by dipolar excitations. Using nonequilibrium dynamical mean field theory, we show that suitably designed chirped pulses may realize this cooling effect. In particular, we demonstrate the emergence of antiferromagnetic order in a system which is initially in a weakly correlated state above the maximum Néel temperature. Our work suggests a general strategy for inducing strong correlation phenomena in periodically modulated atomic gases in optical lattices or light-driven materials.

Quantum Simulation Meets Nonequilibrium Dynamical Mean-Field Theory: Exploring the Periodically Driven, Strongly Correlated Fermi-Hubbard Model.

We perform an abinitio comparison between nonequilibrium dynamical mean-field theory and optical lattice experiments by studying the time evolution of double occupations in the periodically driven Fermi-Hubbard model. For off-resonant driving, the range of validity of a description in terms of an effective static Hamiltonian is determined and its breakdown due to energy absorption close to resonance is demonstrated. For near-resonant driving, we investigate the response to a change in driving amplitude and discover an asymmetric excitation spectrum with respect to the detuning. In general, we find good agreement between experiment and theory, which cross validates the experimental and numerical approaches in a strongly correlated nonequilibrium system.

Entropy-cooled nonequilibrium states of the Hubbard model

We show that the recently proposed cooling-by-doping mechanism allows to efficiently prepare interesting nonequilibrium states of the Hubbard model. Using nonequilibrium dynamical mean field theory and a particle-hole symmetric setup with dipolar excitations to full and empty bands we produce cold photo-doped Mott insulating states with a sharp Drude peak in the optical conductivity, a superconducting state in the repulsive Hubbard model with an inverted population, and $\eta$-paired states in systems with a large density of doublons and holons. The reshuffling of entropy into full and empty bands not only provides an efficient cooling mechanism, it also allows to overcome thermalization bottlenecks and slow dynamics that have been observed in systems cooled by the coupling to boson baths.

Ultrafast Spin Dynamics in Photodoped Spin-Orbit Mott Insulator Sr2IrO4

Ultrafast photodoping of the Mott insulators, possessing strong correlation between electronic and magnetic degrees of freedom, holds promise for launching an ultrafast dynamics of spins which cannot be described in terms of conventional models of ultrafast magnetism. Here we study the ultrafast laser-induced dynamics of the magnetic order in a novel spin-orbit Mott insulator Sr2IrO4 featuring an uncompensated pattern of antiferromagnetic spin ordering. Using the transient magneto-optical Kerr effect sensitive to the net magnetization, we reveal that photodoping by femtosecond laser pulses with photon energy above the Mott gap launches melting of the antiferromagnetic order seen as ultrafast demagnetization with a characteristic time of 300 fs followed by a sub-10-ps recovery. Nonequilibrium dynamical mean-field theory calculations based on the single-band Hubbard model confirm that ultrafast demagnetization is primarily governed by the laser-induced generation of electron-hole pairs, although the precise simulated time dependencies are rather different from the experimentally observed ones. To describe the experimental results, here we suggest a phenomenological model which is based on Onsager’s formalism and accounts for the photogenerated electron-hole pairs using the concepts of holons and doublons.

Control of competing superconductivity and charge order by nonequilibrium currents

We study the competing charge-density-wave and superconducting order in the attractive Hubbard model under a voltage bias, using steady-state non-equilibrium dynamical mean-field theory. We show that the charge-density-wave is suppressed in a current-carrying non-equilibrium steady state. This effect is beyond a simple Joule-heating mechanism and a "supercooled" metallic state is stabilized at a non-equilibrium temperature lower than the equilibrium superconducting $T_c$. On the other hand, a current-carrying superconducting state is always in equilibrium. It is not subject to the same non-thermal suppression, and can therefore nucleate out of the supercooled metal, e.g. in a resistive switching experiment. The fact that an electric current can change the relative stability of different phases compared to thermal equilibrium, even when a system appears locally thermal due to electron-eletron scattering, provides a general perspective to control intertwined orders out of equilibrium.

Quantum Boltzmann equation for strongly correlated systems: Comparison to dynamical mean field theory

We investigate the potential of a quantum Boltzmann equation without momentum conservation for description of strongly correlated electron systems out of equilibrium. In a spirit similar to dynamical mean field theory (DMFT), the momentum conservation of the electron-electron scattering is neglected, which yields a time-dependent occupation function for the equilibrium spectral function, even in cases where well-defined quasiparticles do not exist. The main assumption of this method is that the spectral function remains sufficiently rigid under the non-equilibrium evolution. We compare the result of the quantum Boltzmann equation to non-equilibrium DMFT simulations for the case of photo-carrier relaxation in Mott insulators, where processes on very different timescales emerge, i.e., impact ionization, intra-Hubbard-band thermalization, and full thermalization. Since quantum Boltzmann simulations without momentum conservation are computationally cheaper than non-equilibrium DMFT, this method allows the simulation of more complicated systems or devices, and to access much longer times.