Auxiliary master equation approach to non-equilibrium correlated impurities

Abstract

We present a numerical method for the study of correlated quantum impurity problems out of equilibrium, which is particularly suited to address steady state properties within Dynamical Mean Field Theory. The approach, recently introduced in [Arrigoni et al., Phys. Rev. Lett. 110, 086403 (2013)], is based upon a mapping of the original impurity problem onto an auxiliary open quantum system, consisting of the interacting impurity coupled to bath sites as well as to a Markovian environment. The dynamics of the auxiliary system is governed by a Lindblad master equation whose parameters are used to optimize the mapping. The accuracy of the results can be readily estimated and systematically improved by increasing the number of auxiliary bath sites, or by introducing a linear correction. Here, we focus on a detailed discussion of the proposed approach including technical remarks. To solve for the Green's functions of the auxiliary impurity problem, a non-hermitian Lanczos diagonalization is applied. As a benchmark, results for the steady state current-voltage characteristics of the single impurity Anderson model are presented. Furthermore, the bias dependence of the single particle spectral function and the splitting of the Kondo resonance are discussed. In its present form the method is fast, efficient and features a controlled accuracy.

arXiv comment17 pages, 6 figures

References in corpus (88)

• Spintronics: Fundamentals and applications
• Quantum phase transition from a superfluid to a Mott insulator in a gas of ultracold atoms
• The density-matrix renormalization group in the age of matrix product states
• Cold bosonic atoms in optical lattices
• Thermalization and its mechanism for generic isolated quantum systems
• Efficient simulation of one-dimensional quantum many-body systems
• Quantum properties of atomic-sized conductors
• Dependence of Single Molecule Junction Conductance on Molecular Conformation
• Real time evolution using the density matrix renormalization group
• Time-dependent density-matrix renormalization-group using adaptive effective Hilbert spaces
• The Kernel Polynomial Method
• Measurement of the conductance of a hydrogen molecule
• Low Temperature Transport through a Quantum Dot: The Anderson Model out of Equilibrium
• From the Kondo Regime to the Mixed-Valence Regime in a Single-Electron Transistor
• Time-resolved Observation and Control of Superexchange Interactions with Ultracold Atoms in Optical Lattices
• Evidence for a Structurally-driven Insulator-to-metal Transition in VO2: a View from the Ultrafast Timescale
• The Anderson Model out of Equilibrium: Non-Crossing-Approximation Approach to Transport through a Quantum Dot
• The Luttinger model following a sudden interaction switch-on
• Third quantization: a general method to solve master equations for quadratic open Fermi systems
• Interaction Quench in the Hubbard model
• Dynamical phase transition in correlated fermionic lattice systems
• Quantum Many-Body Phenomena in Coupled Cavity Arrays
• Fermionic transport in a homogeneous Hubbard model: Out-of-equilibrium dynamics with ultracold atoms
• Real-time dynamics in Quantum Impurity Systems: A Time-dependent Numerical Renormalization Group Approach
• Mesoscopic quantum transport: Resonant tunneling in the presence of strong Coulomb interaction
• Resonant tunneling through ultrasmall quantum dots: zero-bias anomalies, magnetic field dependence, and boson-assisted transport
• Nonequilibrium dynamical mean-field theory
• Spin Precession and Real Time Dynamics in the Kondo Model: A Time-Dependent Numerical Renormalization-Group Study
• Atomic three-body loss as a dynamical three-body interaction
• Matrix product simulations of non-equilibrium steady states of quantum spin chains
• Nonequilibrium electron transport using the density matrix renormalization group
• Nonequilibrium Transport in Quantum Impurity Models (Bethe-Ansatz for open systems)
• On steady-state currents through nano-devices: a scattering-states numerical renormalization group approach to open quantum systems
• Time-Dependent Mean Field Theory for Quench Dynamics in correlated electron systems
• Iterative real-time path integral approach to nonequilibrium quantum transport
• Tunneling through molecules and quantum dots: master-equation approaches
• Non-Equilibrium Transport through a Kondo-Dot in a Magnetic Field: Perturbation Theory and Poor Man's Scaling
• Nonthermal steady states after an interaction quench in the Falicov-Kimball model
• Nonequilibrium quantum criticality in open electronic systems
• Real-time simulations of nonequilibrium transport in the single-impurity Anderson model
• A perturbative nonequilibrium renormalization group method for dissipative quantum mechanics: Real-time RG in frequency space (RTRG-FS)
• Nonequilibrium functional renormalization group for interacting quantum systems
• Interaction quench in the Hubbard model: Relaxation of the spectral function and the optical conductivity
• Nonequilibrium Dynamical Mean Field Theory: an auxiliary Quantum Master Equation approach
• Weak-coupling quantum Monte Carlo calculations on the Keldysh contour: theory and application to the current-voltage characteristics of the Anderson model
• Long-range Kondo signature of a single magnetic impurity
• Scaling and Decoherence in the Out-of-Equilibrium Kondo Model
• Kondo resonances and anomalous gate dependence of electronic conduction in single-molecule transistors
• Comparative study of theoretical methods for nonequilibrium quantum transport
• Super-fermion representation of the Lindblad master equation for the electron transport problem
• Quenching Bloch oscillations in a strongly correlated material
• Real-time renormalization group and charge fluctuations in quantum dots
• Functional renormalization group for non-equilibrium quantum many-body problems
• Universal aspects of non-equilibrium currents in a quantum dot
• Sparse polynomial space approach to dissipative quantum systems: Application to the sub-ohmic spin-boson model
• Charge transport through single molecules, quantum dots, and quantum wires
• Perturbative Approach to the Nonequilibrium Kondo Effect in a Quantum Dot
• Superoperator nonequilibrium Green's function theory of many-body systems; Applications to charge transfer and transport in open junctions
• Imaginary-time formulation of steady-state nonequilibrium: application to strongly correlated transport
• Probing the Kondo density of states in a three-terminal quantum ring
• The Kondo Effect in Non-Equilibrium Quantum Dots: Perturbative Renormalization Group
• Steady-state nonequilibrium density of states of driven strongly correlated lattice models in infinite dimensions
• Comparative study of many-body perturbation theory and time-dependent density functional theory in the out-of-equilibrium Anderson model
• Time scales in the dynamics of an interacting quantum dot
• Universal out-of-equilibrium Transport in Kondo-correlated quantum dots: Renormalized dual Fermions on the Keldysh contour
• Dimensional Crossover Driven by an Electric Field
• Emission characteristics of laser-driven dissipative coupled-cavity systems
• Universal lineshape of the Kondo zero-bias anomaly in a quantum dot
• Wilson chains are not thermal reservoirs
• Nonequilibrium transport and optical properties of model metal--Mott-insulator--metal heterostructures
• Hamiltonian-based impurity solver for nonequilibrium dynamical mean-field theory
• Anderson impurity model in nonequilibrium: analytical results versus quantum Monte Carlo data
• Nonequilibrium Dynamics of Anisotropic Large Spins in the Kondo Regime: Time-Dependent Numerical Renormalization Group Analysis
• Quantum simulation of manybody effects in steady-state nonequilibrium: electron-phonon coupled quantum dots
• Nonequilibrium steady state for strongly-correlated many-body systems: variational cluster approach
• Continuous-Time Quantum Monte Carlo and Maximum Entropy Approach to an Imaginary-Time Formulation of Strongly Correlated Steady-State Transport
• Effective Equilibrium Description of Nonequilibrium Quantum Transport I: Fundamentals and Methodology
• Effective Equilibrium Theory of Nonequilibrium Quantum Transport
• Slave-boson Keldysh field theory for the Kondo effect in quantum dots
• Nonequilibrium conductance through a benzene molecule in the Kondo regime
• Steady-state spectra, current and stability diagram of a quantum dot: a non-equilibrium Variational Cluster Approach
• Nonequilibrium self-energy functional theory
• Magnetic field effects on the finite-frequency noise and ac conductance of a Kondo quantum dot out of equilibrium
• Search for the πResonance in Two Particle Tunneling Experiments of YBCO Superconductors
• Imaginary-time quantum many-body theory out of equilibrium I: Formal equivalence to Keldysh real-time theory and calculation of static properties
• Steady-state and quench dependent relaxation of a quantum dot coupled to one-dimensional leads
• The dark side of benzene: interference vs. interaction
• Imaginary-time quantum many-body theory out of equilibrium II: Analytic continuation of dynamic observables and transport properties

Cited by in corpus (98)

• How to discretize a quantum bath for real-time evolution
• Auxiliary master equation approach within matrix product states: Spectral properties of the nonequilibrium Anderson impurity model
• Generalized theory of pseudomodes for exact descriptions of non-Markovian quantum processes
• Lindblad-Driven Discretized Leads for Non-Equilibrium Steady-State Transport in Quantum Impurity Models: Recovering the Continuum Limit
• Tensor-network method to simulate strongly interacting quantum thermal machines
• Imaginary-time matrix product state impurity solver for dynamical mean-field theory
• Green's function methods for single molecule junctions
• An efficient method for quantum impurity problems out of equilibrium
• Non-equilibrium quantum impurity problems via matrix-product states in the temporal domain
• Dynamics of Kondo voltage splitting after a quantum quench
• Optimized auxiliary representation of a non-Markovian environment by a Lindblad equation
• Generic transport formula for a system driven by Markovian reservoirs
• Voltage quench dynamics of a Kondo system
• Efficient low temperature simulations for fermionic reservoirs with the hierarchical equations of motion method: Application to the Anderson impurity model
• Non-Markovian Quantum Mpemba effect
• Spectral functions and negative density of states of a driven-dissipative nonlinear quantum resonator
• Markovian Treatment of non-Markovian Dynamics of Open Fermionic Systems
• Time evolution of the Kondo resonance in response to a quench
• Quantum Boltzmann equation for strongly correlated systems: comparison to dynamical mean field theory
• Open System Tensor Networks and Kramers' Crossover for Quantum Transport
• Configuration interaction based nonequilibrium steady state impurity solver
• A quantum-classical decomposition of Gaussian quantum environments: a stochastic pseudomode model
• Lead Geometry and Transport Statistics in Molecular Junctions
• Many-Body Open Quantum Systems
• Thermoelectric response of a correlated impurity in the nonequilibrium Kondo regime
• Quasi-Lindblad pseudomode theory for open quantum systems
• Impact ionization processes in the steady state of a driven Mott insulating layer coupled to metallic leads
• Quantum thermodynamics with fast driving and strong coupling via the mesoscopic leads approach
• A pseudo-fermion method for the exact description of fermionic environments: from single-molecule electronics to Kondo resonance
• Auxiliary master equation for nonequilibrium dual-fermion approach
• Photo-induced nonequilibrium states in Mott insulators
• Pseudogap Anderson impurity model out of equilibrium: A master equation tensor network approach
• Nonequilibrium Kondo effect in a magnetic field: Auxiliary master equation approach
• Surrogate model solver for impurity-induced superconducting subgap states
• Transport Through a Correlated Interface: Auxiliary Master Equation Approach
• A quantum algorithm for solving open system dynamics on quantum computers using noise
• Build-up of the Kondo effect from real-time 2PI effective action for the Anderson impurity model
• Time-dependent numerical renormalization group method for multiple quenches: towards exact results for the long time limit of thermodynamic observables and spectral functions
• Performance of Reservoir Discretizations in Quantum Transport Simulations
• Feynman-Vernon influence functional approach to quantum transport in interacting nanojunctions: An analytical hierarchical study
• Tensor network influence functionals in the continuous-time limit: connections to quantum embedding, bath discretization, and higher-order time propagation
• Diagrammatic Monte Carlo for Dissipative Quantum Impurity Models
• A Green's function approach to the linear response of a driven dissipative optomechanical system
• Analytic expressions for the steady-state current with finite extended reservoirs
• Modeling the unphysical pseudomode model with physical ensembles: simulation, mitigation, and restructuring of non-Markovian quantum noise
• Nonequilibrium Kondo effect by equilibrium numerical renormalization group method: The hybrid Anderson model subject to a finite spin bias
• Accumulative reservoir construction: Bridging continuously relaxed and periodically refreshed extended reservoirs
• Correlated Mott insulators in strong electric fields: Role of phonons in heat dissipation
• Impact ionization processes in a photodriven Mott insulator: influence of phononic dissipation
• Negative cavity photon spectral function in an optomechanical system with two parametrically-driven mechanical modes
• Charge redistribution in correlated heterostuctures within nonequilibrium real-space dynamical mean-field theory
• Kondo-Zeno crossover in the dynamics of a monitored quantum dot
• Entropy production in the mesoscopic-leads formulation of quantum thermodynamics
• Simulating Lindbladian evolution with non-abelian symmetries: Ballistic front propagation in the $SU(2)$ Hubbard model with a localized loss
• Minimal pole representation for spectral functions
• Resonance Effects in Correlated Multilayer Heterostructures
• Correlation versus dissipation in a non-Hermitian Anderson impurity model
• Auxiliary master equation approach within stochastic wave functions: Application to the Interacting Resonant Level Model
• Mixed-order symmetry-breaking quantum phase transition far from equilibrium
• Density-wave steady-state phase of dissipative ultracold fermions with nearest-neighbor interactions
• Correlated Mott insulators in a strong electric field: The effects of phonon renormalization
• Coupled Lindblad pseudomode theory for simulating open quantum systems
• Master equation based steady-state cluster perturbation theory
• Extracting Dynamical Maps of Non-Markovian Open Quantum Systems
• Grassmann time-evolving matrix product operators: An efficient numerical approach for fermionic path integral simulations
• Transport in a periodically driven tilted lattice via the extended reservoir approach: Stability criterion for recovering the continuum limit
• Many-body wavefunctions for quantum impurities out of equilibrium. I. The nonequilibrium Kondo model
• First-principles molecular transport calculation for the benzenedithiolate molecule
• Information Loss Pathways in a Numerically Exact Simulation of a non-Markovian Open Quantum System
• Dressed Quantum Trajectories: Novel Approach to the non-Markovian Dynamics of Open Quantum Systems on a Wide Time Scale
• Spectral Density Modulation and Universal Markovian Closure of Fermionic Environments
• Efficient Pseudomode Representation and Complexity of Quantum Impurity Models
• Thermoelectric properties of a strongly correlated layer
• Non-equilibrium boundary driven quantum systems: models, methods and properties
• Many-body wavefunctions for quantum impurities out of equilibrium
• A comprehensive study of out-of-equilibrium Kondo effect and Coulomb blockade
• Input-Output Hierarchical Equations Of Motion
• Impact of disorder and phonons on the Hubbard bands of Mott insulators in strong electric fields
• Diffusion and Thermalization in a Boundary-Driven Dephasing Model
• Mixed-configuration approximation for multiorbital systems out of equilibrium
• Photodriven Mott insulating heterostructures: A steady-state study of impact ionization processes
• Non-equilibrium Green's functions and their relation to the negative differential conductance in the interacting resonant level model
• Simulating electron-vibron energy transfer with quantum dots and resonators
• Non-equilibrium variational cluster perturbation theory: quench dynamics of the quantum Ising model
• Steady-State Quantum Zeno Effect of Driven-Dissipative Bosons with Dynamical Mean-Field Theory
• Scalable Effective Models for Superconducting Nanostructures: Applications to Double, Triple, and Quadruple Quantum Dots
• Iterated Perturbation Theory for Mott Insulators in a Static Electric Field with Optical Phonons
• Nonequilibrium transport through an interacting monitored quantum dot
• Dual current anomalies and quantum transport within extended reservoir simulations
• Mean Field Decoupling of Single Impurity Anderson Model through Auxiliary Majorana Fermions
• Approaching the scaling limit of transport through lattices with dephasing
• Beyond mean-field dynamics of the Dicke model with non-Markovian dephasing
• Dissipative Kondo physics in the Anderson Impurity Model with two-body losses
• Synchronizing microwave cQED limit-cycle oscillators
• Exact description of fermionic reservoirs via purified damped ancillary fermions
• Subtleties in the pseudomodes formalism
• Process Tensor Approaches to Non-Markovian Quantum Dynamics
• Steady-state dc transport through an Anderson impurity coupled to leads with spin-orbit coupling