Nonequilibrium dynamical mean-field theory and its applications

Abstract

The study of nonequilibrium phenomena in correlated lattice systems has developed into an active and exciting branch of condensed matter physics. This research field provides rich new insights that could not be obtained from the study of equilibrium situations, and the theoretical understanding of the physics often requires the development of new concepts and methods. On the experimental side, ultra-fast pump-probe spectroscopies enable studies of excitation and relaxation phenomena in correlated electron systems, while ultra-cold atoms in optical lattices provide a new way to control and measure the time-evolution of interacting lattice systems with a vastly different characteristic timescale compared to electron systems. A theoretical description of these phenomena is challenging because, firstly, we have to compute the quantum-mechanical time-evolution of many-body systems out of equilibrium, and secondly, deal with strong-correlation effects which can be of nonperturbative nature. In this review, we discuss the nonequilibrium extension of the dynamical mean field theory (DMFT), which treats quantum fluctuations in the time domain and works directly in the thermodynamic limit. The method reduces the complexity of the calculation via a mapping to a self-consistent impurity problem. Particular emphasis is placed on a detailed derivation of the formalism, and on a discussion of numerical techniques, which enable solutions of the effective nonequilibrium DMFT impurity problem. We summarize the insights gained into the properties of the infinite-dimensional Hubbard model under strong non-equilibrium conditions. These examples illustrate the current ability of the theoretical framework to reproduce and understand fundamental nonequilibrium phenomena, such as the dielectric breakdown of Mott insulators, photo-doping, and collapse-and-revival oscillations in quenched systems.

Review article, including sample programs

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• The relationship between Hirsch-Fye and weak coupling diagrammatic Quantum Monte Carlo methods
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• Kinetic description of thermalization dynamics in weakly interacting quantum systems
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• Nonequilibrium charge transport through Falicov-Kimball structures connected to metallic leads
• Nonequilibrium RIXS study of an electron-phonon model
• Dynamical spin-to-charge conversion on the edge of quantum spin Hall insulator
• Dynamically induced doublon repulsion in the Fermi-Hubbard model probed by a single-particle density of states
• Boltzmann relaxation dynamics of strongly interacting spinless fermions on a lattice
• Comparison of the Iterated Equation of Motion Approach and the Density Matrix Formalism for the Quantum Rabi Model
• $\text{Ab initio}$ dynamical mean-field theory with natural orbitals renormalization group impurity solver: Formalism and applications
• The Streda Formula for Floquet Systems: Topological Invariants and Quantized Anomalies from Cesaro Summation
• Solvable entanglement dynamics in quantum circuits with generalized space-time duality
• Periodically driven interacting electrons in 1D: a many-body Floquet approach
• Suppression of Heating by Multi-color Driving Protocols in Floquet Engineered Strongly Correlated Systems
• Nonequilibrium self-energy functional approach to the dynamical Mott transition
• Work statistics across a quantum critical surface
• Nature of the photo-induced metallic state in monoclinic VO${}_2$
• Real-time evolution of static electron-phonon models in time-dependent electric fields
• Proposed Fermi-surface reservoir-engineering and application to realizing unconventional Fermi superfluids in a driven-dissipative non-equilibrium Fermi gas
• Nonequilibrium phases and phase transitions of the XY-model
• Mechanism for Negative Differential Conductivity in Holographic Conductors
• (Non equilibrium) Thermodynamics of Integrable models: The Generalized Gibbs Ensemble description of the classical Neumann Model
• Impurity States and Indirect Exchange Interaction in Irradiated Graphene
• Electrically driven insulator-to-metal transition in a correlated insulator: Electronic mechanism and thermal description
• Stochastic semiclassical theory for non-equilibrium electron-phonon coupled systems
• Hierarchy of double-time correlations
• Floquet-driven indirect exchange interaction mediated by topological insulator surface states
• Revealing Hund's multiplets in Mott insulators under strong electric fields
• Efficient computation of the second-Born self-energy using tensor-contraction operations
• Stark-Many body localization in interacting infinite dimensional systems
• Keldysh field theory of a driven dissipative Mott insulator: nonequilibrium response and phase transitions
• Semi-group influence matrices for non-equilibrium quantum impurity models
• Steady-state dynamical mean field theory based on influence functional matrix product states
• Predicted photoinduced pair annihilation of emergent magnetic charges in the organic salt $\alpha$-(BEDT-TTF)${}_2$I${}_3$ irradiated by linearly polarized light
• Resonance Effects in Correlated Multilayer Heterostructures
• Photoinduced charge carrier dynamics in Hubbard two-leg ladders and chains
• Photo-induced Dirac cone flattening in BaNiS${}_2$
• Unexpected linear conductivity in Landau-Zener model: limitations and improvements of the relaxation time approximation in the quantum master equation
• Correlated Mott insulators in a strong electric field: The effects of phonon renormalization
• Nonequilibrium Quantum Critical Steady State: Transport Through a Dissipative Resonant Level
• Light-induced Floquet spin-triplet Cooper pairs in unconventional magnets
• Charge and pairing dynamics in the attractive Hubbard model: mode coupling and the validity of linear-response theory
• Photoinduced prethermal order parameter dynamics in the two-dimensional large-$N$ Hubbard-Heisenberg model
• Strong quenches in the one-dimensional Fermi-Hubbard model
• Mixed-order symmetry-breaking quantum phase transition far from equilibrium
• Floquet States
• Steady off-diagonal long-range order state in a half-filled dimerized Hubbard chain induced by a resonant pulsed field
• Field theory for the dynamics of the open $O(N)$ model
• Exact real-time dynamics of single-impurity Anderson model from a single-spin hybridization-expansion
• Coupled Lindblad pseudomode theory for simulating open quantum systems
• Dynamic pathway of the photoinduced phase transition of TbMnO${}_3$
• Local interpretation of time-resolved X-ray absorption in Mott insulators: Insights from nonequilibrium dynamical mean-field theory
• Analysis of time-resolved single-particle spectrum on the one-dimensional extended Hubbard model
• Mode attraction in Floquet systems with memory: application to magnonics
• Dicke Phase Transition in a Disordered Emitter-Graphene Plasmon System
• Unraveling long-time quantum dynamics using flow equations
• Memory-Efficient Nonequilibrium Green's Function Framework Built On Quantics Tensor Trains
• Density-wave steady-state phase of dissipative ultracold fermions with nearest-neighbor interactions
• Rate equation analysis on the dynamics of first-order exciton Mott transition
• Anderson impurity solver integrating tensor network methods with quantum computing
• Strong terahertz third-harmonic generation by kinetic heavy quasiparticles in CaRuO${}_3$
• Thermalization of isolated Bose-Einstein condensates by dynamical heat bath generation
• Nanoscopic time crystal obtained by nonergodic spin dynamics
• TR-ARPES Signal in Pumped Semiconductors within Dynamical Projective Operatorial Approach (DPOA)
• Site-selective doublon-holon dynamics in a pumped one-dimensional Hubbard superlattice with staggered Coulomb interactions
• Grassmann time-evolving matrix product operators: An efficient numerical approach for fermionic path integral simulations
• Master equation based steady-state cluster perturbation theory
• Photon-Induced Suppression of Interlayer Tunneling in Van Der Waals Heterostructures
• Nonequilibrium response of an electron mediated charge-density-wave-ordered material to a large dc electric field
• Dynamical mean-field theory for Rényi entanglement entropy and mutual Information in Hubbard Model
• Emergence of Larkin-Ovchinnikov-type superconducting state in a voltage-driven superconductor
• Review of recent developments of the functional renormalization group for systems out of equilibrium
• Orbital-selective thermalization plateau in the mass imbalanced Hubbard model
• Photoexcitations in the Hubbard model -- generalized Loschmidt amplitude analysis of impact ionization in small clusters
• Multidimensional coherent spectroscopy of correlated lattice systems
• Light-induced hidden odd-frequency order in a model for A${}_3$C${}_{60}$
• Towards numerically exact computation of conductivity in the thermodynamic limit of interacting lattice models
• Predicted novel type of photoinduced topological phase transition accompanied by collision and collapse of Dirac-cone pair in organic salt $\alpha$-(BEDT-TTF)${}_2$I${}_3$
• Impurity Screening and Friedel Oscillations in Floquet-driven Two-dimensional Metals
• Photoinduced prethermalization phenomena in correlated metals
• Efficient Magnus-type integrators for solar energy conversion in Hubbard models
• Twisted light-induced spin-spin interaction in a chiral helimagnet
• Comparing scattering rates from Boltzmann and dynamical mean-field theory
• Hierarchy of correlations: Application to Green's functions and interacting topological phases
• Photoinduced 120-degree spin order in the Kondo-lattice model on a triangular lattice
• Flat bands in condensed-matter systems -- perspective for magnetism and superconductivity
• Dynamical Mean-Field Theory description of the voltage induced transition in a non-equilibrium superconductor
• Photo-induced insulator-metal transition in paramagnetic (V${}_{1-x}$Cr${}_x$)${}_2$O${}_3$
• Dressed Quantum Trajectories: Novel Approach to the non-Markovian Dynamics of Open Quantum Systems on a Wide Time Scale
• Loading and detecting a three-dimensional Fermi gas in one-dimensional optical superlattice
• Adaptive variational quantum computing approaches for Green's functions and nonlinear susceptibilities
• Information Loss Pathways in a Numerically Exact Simulation of a non-Markovian Open Quantum System
• Efficient Pseudomode Representation and Complexity of Quantum Impurity Models
• On optical spectroscopy of molecular junctions
• Asymmetry-induced radiative heat transfer in Floquet systems
• Numerical renormalization of glassy dynamics
• Transport in Conductors and Rectifiers: Mean-Field Redfield Equations and Non-Equilibrium Green's Functions
• Quantifying spatio-temporal patterns in classical and quantum systems out of equilibrium
• Thermalization of a Closed Sachdev-Ye-Kitaev System in the Thermodynamic Limit
• Electron-magnon dynamics triggered by an ultrashort laser pulse: A real-time Dual $GW$ study
• The perils of minimal coupling to electromagnetic field in quantum many-body systems
• Superconducting optical response of photodoped Mott insulators
• Photo-excited states in correlated band insulators
• Fate of the Mollow triplet in strongly-coupled atomic arrays
• Spin correlations in the bilayer Hubbard model with perpendicular electric field
• Interacting electrons in a flat-band system within the Generalized Kadanoff-Baym Ansatz
• On the stability of dissipatively-prepared Mott insulators of photons
• Floquet theory and applications in open quantum and classical systems
• Ultra-fast electric field controlled spin-fluctuations in the Hubbard model
• Nonequilibrium Green's functions for functional connectivity in the brain
• Strange metallicity in an antiferromagnetic quantum critical model: A sign-problem-free quantum Monte-Carlo study
• Attraction versus repulsion between doublons or holons in Mott-Hubbard systems
• Excited States beyond Mott Gap in Half-Filled-Band Hubbard Model
• Path Integral Formalism for Quantum Open Systems
• Real-space renormalized dynamical mean field theory
• The anomalous Floquet Anderson insulator in a continuously driven optical lattice
• Time-resolved photoemission and RIXS study of a site-selective Mott insulator
• Out of Time Order Correlation of the Hubbard Model with Random Local Disorder
• Conductance of a Dissipative Quantum Dot: Nonequilibrium Crossover Near a Non-Fermi-Liquid Quantum Critical Point
• Measuring the ultrafast screening of $U$ in photo-excited charge-transfer insulators with time-resolved X-ray absorption spectroscopy
• Transient dynamics and quantum phase diagram for the square lattice Rashba-Hubbard model at arbitrary hole doping
• A new pathway to impact ionization in a photo-excited one-dimensional ionic Hubbard model
• Tensor cross interpolation approach for quantum impurity problems based on the weak-coupling expansion
• Dynamical recovery of SU(2) symmetry in the mass-quenched Hubbard model
• Photo-induced Dynamics of Quasicrystalline Excitonic Insulator
• Monolayer transition metal dichalcogenides under finite-pulse polarized radiation
• Spatial behavior in a Mott insulator near the voltage-driven resistive transition
• A comprehensive study of out-of-equilibrium Kondo effect and Coulomb blockade
• Theory of Photocurrent and High-Harmonic Generation with Chiral Fermions
• Impact of disorder and phonons on the Hubbard bands of Mott insulators in strong electric fields
• Self-energy method for time-dependent spectral functions of the Anderson impurity model within the time-dependent numerical renormalization group approach
• Compact representation and long-time extrapolation of real-time data for quantum systems using the ESPRIT algorithm
• Symmetry-protected Bose-Einstein condensation of interacting hardcore Bosons
• Time-dependent Mott transition in the periodic Anderson model with nonlocal hybridization
• Nonequilibrium DMFT approach to time-resolved Raman spectroscopy
• Many-body tunneling in a double-well potential
• Photo-induced charge, spin, and orbital order in the two-orbital extended Hubbard model
• Floquet Control of Indirect Exchange Interaction in Periodically Driven Two-Dimensional Electron Systems
• Dynamical Triplet Unravelling: A quantum Monte Carlo algorithm for reversible dynamics
• Thermoelectric energy conversion in molecular junctions out of equilibrium
• Approximating dynamical correlation functions with constant depth quantum circuits
• Disorder Enhanced Thermalization in Interacting Many-Particle System
• Phases of translation-invariant systems out of equilibrium: Iterative Green's function techniques and renormalization group approaches
• A General Strategy for Realizing Mpemba Effects in Open Quantum Systems
• Momentum-dependent relaxation dynamics of the doped repulsive Hubbard model
• Correspondence between quasiparticle dissipation and quantum information decay in open quantum systems
• Quantum Thermalization via Travelling Waves
• Multiple Floquet Chern insulator phases in the spin-charge coupled triangular-lattice ferrimagnet: Crucial role of higher-order terms in the high-frequency expansion
• Quench dynamics in the one-dimensional mass-imbalanced ionic Hubbard model
• Third-order strong-coupling impurity solver for real-frequency DMFT: Accurate spectral functions for antiferromagnetic and photo-doped states
• Mixed-configuration approximation for multiorbital systems out of equilibrium
• Nonequilibrium electron distribution function in a voltage-biased nanowire: A nonequilibrium Green's function approach
• Stability of Floquet sidebands and quantum coherence in 1D strongly interacting spinless fermions
• Stochastic Wave-Function Simulation of Irreversible Emission Processes for Open Quantum Systems in a Non-Markovian Environment
• Systematic large flavor fTWA approach to interaction quenches in the Hubbard model
• Infinite Grassmann time-evolving matrix product operators for quantum impurity problems after a quench
• Decoding the drive-bath interplay: A guideline to enhance superconductivity
• Dynamic inhomogeneities and phase separation after quantum quenches in strongly correlated systems
• Iterated Perturbation Theory for Mott Insulators in a Static Electric Field with Optical Phonons
• Floquet DMFT Analysis of High Harmonic Generation in Mott Insulators
• Nodal Spectral Functions Stabilized by Non-Hermitian Topology of Quasiparticles
• Distinct charge and spin recovery dynamics in a photo-excited Mott insulator
• Kondo spectral functions at low-temperatures: A dynamical-exchange-correlation-field perspective
• Terahertz harmonic generation across the Mott insulator-metal transition
• Problem of nonlinear conductivity within relaxation time approximation in noncentrosymmetric insulators
• Multi-tunneling effect of nonreciprocal Landau-Zener tunneling: Insights from DC field responses
• Electron transport in disordered insulating lattice under nonlinear electric field
• Spectral properties of disordered insulating lattice under nonlinear electric field
• Universal non-equilibrium dynamics of pure states and density-dependent thermalization in Sachdev-Ye-Kitaev model
• Formulation of the orbital magnetic moment in multiorbital tight-binding models: Application to the inverse Faraday effect
• Scalable tensor network algorithm for quantum impurity problems
• Summing Real Time Feynman Paths of Lattice Polaron with Matrix Product States
• Non-equilibrium variational cluster perturbation theory: quench dynamics of the quantum Ising model
• A causality-based divide-and-conquer algorithm for nonequilibrium Green's function calculations with quantics tensor trains
• Two-dimensional coherent spectroscopy of disordered superconductors in the narrow-band and broad-band limits
• Steady-State Quantum Zeno Effect of Driven-Dissipative Bosons with Dynamical Mean-Field Theory
• Energy flow during relaxation in an electron-phonon system with multiple modes: A nonequilibrium Green's function study
• Time-resolved single-particle spectrum of the one-dimensional extended Hubbard model after interaction quenches
• Nonequilibrium thermal state of a voltage-biased Mott insulator
• Orbital liquid in the $e_g$ orbital Hubbard model in $d=\infty$ dimensions
• Field induced conducting state in Mott insulator
• Nonequilibrium-DMFT based RIXS investigation of the two-orbital Hubbard model
• Characterizing Featureless Mott Insulating State by Quasiparticle Interferences - A Dynamical Mean Field Theory Prospect
• Photo-induced Non-collinear Interlayer RKKY Coupling in Bulk Rashba Semiconductors
• Photoinduced excitonic magnetism in a multiorbital Hubbard system
• Light-induced shear phonon splitting and instability in bilayer graphene
• Laser-Induced Commensurate-Incommensurate Transition of Charge Order in a Hubbard Superlattice
• Photoinduced melting dynamics and collective mode in a correlated charge-ordered system
• Time-dependent variational Monte Carlo study of the dynamic response of bosons in an optical lattice
• Process Tensor Approaches to Non-Markovian Quantum Dynamics
• Toward nonthermal control of excited quantum materials: framework and investigations by ultrafast electron scattering and imaging
• Electronic modes induced by spin and charge perturbations in Mott and Kondo insulators
• Dissipative Kondo physics in the Anderson Impurity Model with two-body losses
• Ultrafast metal-to-insulator switching in a strongly correlated system
• Enforcing conservation laws in nonequilibrium cluster perturbation theory
• Current-induced successive structural phase transitions beyond thermal equilibrium in single-crystal VO2
• Scrambled Mean Field Approach to the Quantum Dynamics of Degenerate Bose Gases
• Universal quench dynamics of lattice $q$ fermion Yukawa Sachdev-Ye-Kitaev model
• Interaction effects on electronic Floquet spectra: Excitonic effects
• Ultrafast Electronic Structure Engineering in 1$T$-TaS${}_2$: Role of Doping and Amplitude Mode Dynamics
• Mean Field Decoupling of Single Impurity Anderson Model through Auxiliary Majorana Fermions
• Interaction quenches in Bose gases studied with a time-dependent hypernetted-chain Euler-Lagrange method
• Generalised Gibbs Ensemble for spherically constrained harmonic models
• Nonequilibrium hysteretic phase transitions in periodically light-driven superconductors
• Light Control of Triplet Pairing in Correlated Electrons with Mixed-Sign Interactions
• Enhancement of superconducting pairing via quantum Lyapunov control
• Theory of Tunneling between Two-Dimensional Electron Layers Driven by Spin Pumping: Adiabatic Regime and Beyond
• Non-equilibrium Green's function formalism for radiative heat transfer
• Tangent equations of motion for nonlinear response functions
• Fermionic-propagator and alternating-basis quantum Monte Carlo methods for correlated electrons on a lattice
• Algorithm for computing perturbation series of dynamical mean field theory
• Many-body correlations in Floquet steady-states: Frequency-resolved renormalization group of the driven Anderson impurity
• Insulating-to-conducting state transition in the bilayer Hubbard model induced by a perpendicular quench field
• Nonequilibrium Pump-Probe Photoexcitation as a Tool for Analyzing Unoccupied Equilibrium States of Correlated Electrons
• Charge carrier relaxation dynamics in the one-dimensional Kondo lattice model