Infinite Grassmann Time-Evolving Matrix Product Operator Method in the Steady State

Abstract

We present an infinite Grassmann time-evolving matrix product operator method for quantum impurity problems, which directly works in the steady state. The method embraces the well-established infinite matrix product state algorithms with the recently developed GTEMPO method, and benefits from both sides: it obtains real-time Green's functions without sampling noises and bath discretization error, it is applicable for any temperature without the sign problem, its computational cost is independent of the transient dynamics and does not scale with the number of baths. We benchmark the method on the finite-temperature equilibrium Green's function in the noninteracting limit against exact solutions and in the single-orbital Anderson impurity model against GTEMPO calculations. We also study the zero-temperature non-equilibrium steady state of an impurity coupled to two baths with a voltage bias, obtaining consistent particle currents with existing calculations. The method is ideal for studying steady-state quantum transport, and can be readily used as an efficient real-time impurity solver in the dynamical mean field theory and its non-equilibrium extension.

11 pages, 7 figures

References in corpus (26)

• The density-matrix renormalization group in the age of matrix product states
• Continuous-time Monte Carlo methods for quantum impurity models
• Classical simulation of infinite-size quantum lattice systems in one spatial dimension
• The iTEBD algorithm beyond unitary evolution
• Hybridization expansion impurity solver: General formulation and application to Kondo lattice and two-orbital models
• Time-evolving a matrix product state with long-ranged interactions
• 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
• Spectral functions in one-dimensional quantum systems at T>0
• Real-time simulations of nonequilibrium transport in the single-impurity Anderson model
• Twofold advance in the theoretical understanding of far-from-equilibrium properties of interacting nanostructures
• Solving nonequilibrium dynamical mean-field theory using matrix product states
• Sum-rules and bath-parametrization for quantum cluster theories
• Chebyshev Matrix Product State Impurity Solver for the Dynamical Mean-Field Theory
• Chebyshev expansion for Impurity Models using Matrix Product States
• Open Quantum System Dynamics from Infinite Tensor Network Contraction
• A partial fraction decomposition of the Fermi function
• The Hidden Phase of the Spin-Boson Model
• Anderson impurity model in nonequilibrium: analytical results versus quantum Monte Carlo data
• Kondo model in nonequilibrium: Interplay between voltage, temperature, and crossover from weak to strong coupling
• Grassmann Time-Evolving Matrix Product Operators for Quantum Impurity Models
• Natural Orbitals Renormalization Group Approach to the Two-Impurity Kondo Critical Point
• Keldysh effective action theory for universal physics in spin-1/2 Kondo dots
• Grassmann Time-Evolving Matrix Product Operators for Equilibrium Quantum Impurity Problems
• Real-time Impurity Solver Using Grassmann Time-Evolving Matrix Product Operators
• Nonequilibrium quantum dynamics of the magnetic Anderson model

Cited by in corpus (8)

• Correlation Functions From Tensor Network Influence Functionals: The Case of the Spin-Boson Model
• Solving quantum impurity problems on the L-shaped Kadanoff-Baym contour
• Semi-group influence matrices for non-equilibrium quantum impurity models
• Grassmann time-evolving matrix product operators: An efficient numerical approach for fermionic path integral simulations
• Infinite Grassmann time-evolving matrix product operator method for zero-temperature equilibrium quantum impurity problems
• Infinite Grassmann time-evolving matrix product operators for quantum impurity problems after a quench
• Uniform process tensor approach for the calculation of multi-time correlation functions of non-Markovian open systems
• Process Tensor Approaches to Non-Markovian Quantum Dynamics