Quantum Monte Carlo in the steady-state

Abstract

We present a numerically exact steady-state inchworm Monte Carlo method for nonequilibrium quantum impurity models. Rather than propagating an initial state to long times, the method is directly formulated in the steady-state. This eliminates any need to traverse the transient dynamics and grants access to a much larger range of parameter regimes at vastly reduced computational costs. We benchmark the method on equilibrium Green's functions of quantum dots in the noninteracting limit and in the unitary limit of the Kondo regime. We then consider correlated materials described with dynamical mean field theory and driven away from equilibrium by a bias voltage. We show that the response of a correlated material to a bias voltage differs qualitatively from the splitting of the Kondo resonance observed in bias-driven quantum dots.

References in corpus (20)

• Continuous-time Monte Carlo methods for quantum impurity models
• Real time evolution using the density matrix renormalization group
• Real-time dynamics in Quantum Impurity Systems: A Time-dependent Numerical Renormalization Group Approach
• Real-time path integral approach to nonequilibrium many-body quantum system
• Light-induced emergent phenomena in 2D materials and topological materials
• Diagrammatic Monte Carlo simulation of non-equilibrium systems
• Continuous-time auxiliary field Monte Carlo for quantum impurity models
• On steady-state currents through nano-devices: a scattering-states numerical renormalization group approach to open quantum systems
• Optically induced superconductivity in striped La2-xBaxCuO4 by polarization-selective excitation in the near infrared
• Nonequilibrium Dynamical Mean Field Theory: an auxiliary Quantum Master Equation approach
• Electrically-driven phase transition in magnetite nanostructures
• The influence of ultra-fast laser pulses on electron transfer in molecular wires studied by a non-Markovian density matrix approach
• Imaginary-time formulation of steady-state nonequilibrium: application to strongly correlated transport
• Bold Line Diagrammatic Monte Carlo Method: General formulation and application to expansion around the Non-Crossing Approximation
• Inchworm Monte Carlo for exact non-adiabatic dynamics I. Theory and algorithms
• Universal Prony fitting decomposition for optimized hierarchical quantum master equations
• Inchworm Monte Carlo for exact non-adiabatic dynamics II. Benchmarks and comparison with established methods
• Currents and Green's functions of impurities out of equilibrium -- results from inchworm Quantum Monte Carlo
• Multiconfiguration time-dependent Hartree impurity solver for nonequilibrium dynamical mean-field theory
• Quantum Quasi-Monte Carlo algorithm for out-of-equilibrium Green functions at long times

Cited by in corpus (21)

• A Tensor Train Continuous Time Solver for Quantum Impurity Models
• Photo-induced nonequilibrium states in Mott insulators
• Effective-Hamiltonian theory: An approximation to the equilibrium state of open quantum systems
• Diagrammatic Monte Carlo for Dissipative Quantum Impurity Models
• Bath-induced interactions and transient dynamics in open quantum systems at strong coupling: Effective Hamiltonian approach
• Solving quantum impurity problems on the L-shaped Kadanoff-Baym contour
• Infinite Grassmann Time-Evolving Matrix Product Operator Method in the Steady State
• Stark-Many body localization in interacting infinite dimensional systems
• Transient dynamical phase diagram of the spin-boson model
• Grassmann time-evolving matrix product operators: An efficient numerical approach for fermionic path integral simulations
• Extracting Dynamical Maps of Non-Markovian Open Quantum Systems
• Solving Caldeira-Leggett Model by Inchworm Method with Frozen Gaussian Approximation
• Compact representation and long-time extrapolation of real-time data for quantum systems using the ESPRIT algorithm
• Measuring the ultrafast screening of $U$ in photo-excited charge-transfer insulators with time-resolved X-ray absorption spectroscopy
• Simulation of Spin Chains with off-diagonal Coupling Using Inchworm Method
• Denoising of Imaginary Time Response Functions with Hankel projections
• Infinite Grassmann time-evolving matrix product operators for quantum impurity problems after a quench
• Mixed-configuration approximation for multiorbital systems out of equilibrium
• Inchworm tensor train hybridization expansion quantum impurity solver
• Transient Dynamical Phase Diagram of the Spin-Boson Model at Finite Temperature
• Algorithm for computing perturbation series of dynamical mean field theory