Solving quantum impurity problems on the L-shaped Kadanoff-Baym contour
arXiv:2404.05410 · doi:10.1103/PhysRevB.110.165114
Abstract
The path integral formalism is the building block of many powerful numerical methods for quantum impurity problems. However, existing fermionic path integral based numerical calculations have only been performed in either the imaginary-time or the real-time axis, while the most generic scenario formulated on the L-shaped Kadanoff-Baym contour is left unexplored. In this work, we extended the recently developed Grassmann time-evolving matrix product operator (GTEMPO) method to solve quantum impurity problems directly on the Kadanoff-Baym contour. The resulting method is numerically exact, with only two sources of numerical errors, e.g., the time discretization error and the matrix product state bond truncation error. The accuracy of this method is numerically demonstrated against exact solutions in the noninteracting case, and against existing calculations on the real- and imaginary-time axes for the single-orbital Anderson impurity model. We also show that the numerical errors of the method can be well suppressed as we refine the hyperparameters. Our method is a perfect benchmarking baseline for its alternatives which often employ less-controlled approximations, and can also be used as a real-time impurity solver in dynamical mean field theory.
arXiv comment13 pages, 8 figures
References in corpus (55)
- Continuous-time Monte Carlo methods for quantum impurity models
- The numerical renormalization group method for quantum impurity systems
- A continuous-time solver for quantum impurity models
- Nonequilibrium dynamical mean-field theory and its applications
- Continuous Time Quantum Monte Carlo method for fermions
- Exact dynamics of dissipative electronic systems and quantum transport: Hierarchical equations of motion approach
- Hybridization expansion impurity solver: General formulation and application to Kondo lattice and two-orbital models
- Efficient non-Markovian quantum dynamics using time-evolving matrix product operators
- Zero temperature metal-insulator transition in the infinite-dimensional Hubbard model
- Energy resolution and discretization artefacts in the numerical renormalization group
- Continuous-time auxiliary field Monte Carlo for quantum impurity models
- How bad metals turn good: spectroscopic signatures of resilient quasiparticles
- Taming the dynamical sign problem in real-time evolution of quantum many-body problems
- Efficient real frequency solver for dynamical mean field theory
- Variational matrix product state approach to quantum impurity models
- DMFT+NRG study of spin-orbital separation in a three-band Hund's metal
- Dynamical Mean Field Theory with the Density Matrix Renormalization Group
- Nevanlinna Analytical Continuation
- Sum-rules and bath-parametrization for quantum cluster theories
- Green's functions from real-time bold-line Monte Carlo: spectral properties of the nonequilibrium Anderson impurity model
- Chebyshev Matrix Product State Impurity Solver for the Dynamical Mean-Field Theory
- Fork Tensor Product States - Efficient Three Orbital Real Time DMFT Solver
- Chebyshev expansion for Impurity Models using Matrix Product States
- Efficient DMFT impurity solver using real-time dynamics with Matrix Product States
- Green's functions from real-time bold-line Monte Carlo
- Inchworm Monte Carlo for exact non-adiabatic dynamics I. Theory and algorithms
- Dynamics of quantum dissipation systems interacting with Fermion and Boson grand canonical bath ensembles: Hierarchical equations of motion approach
- Inchworm Monte Carlo for exact non-adiabatic dynamics II. Benchmarks and comparison with established methods
- Imaginary-time matrix product state impurity solver for dynamical mean-field theory
- An efficient method for quantum impurity problems out of equilibrium
- Real time evolution of Anderson impurity models via tensor network influence functionals
- Non-equilibrium quantum impurity problems via matrix-product states in the temporal domain
- Doublon-holon origin of the subpeaks at the Hubbard band edges
- Continuous-time hybridization expansion quantum impurity solver for multi-orbital systems with complex hybridizations
- Quantum Renormalization Groups Based on Natural Orbitals
- Adaptive broadening to improve spectral resolution in the numerical renormalization group
- Quantum Monte Carlo in the steady-state
- Efficient hybridization fitting for dynamical mean-field theory via semi-definite relaxation
- A Numerical Renormalization Group approach to Non-Equilibrium Green's Functions for Quantum Impurity Models
- Multiorbital Quantum Impurity Solver for General Interactions and Hybridizations
- Distributional exact diagonalization formalism for quantum impurity models
- Efficient mapping for Anderson impurity problems with matrix product states
- Natural-Orbital Impurity Solver and Projection Approach for Green's Function
- Configuration interaction based nonequilibrium steady state impurity solver
- libdlr: Efficient imaginary time calculations using the discrete Lehmann representation
- Grassmann Time-Evolving Matrix Product Operators for Quantum Impurity Models
- Natural Orbitals Renormalization Group Approach to the Two-Impurity Kondo Critical Point
- A fast time domain solver for the equilibrium Dyson equation
- Beyond the Hubbard bands in strongly correlated lattice bosons
- Equilibrium Quantum Impurity Problems via Matrix Product State Encoding of the Retarded Action
- Excitations and spectra from equilibrium real-time Green's functions
- Grassmann Time-Evolving Matrix Product Operators for Equilibrium Quantum Impurity Problems
- Real-time Impurity Solver Using Grassmann Time-Evolving Matrix Product Operators
- Infinite Grassmann Time-Evolving Matrix Product Operator Method in the Steady State
- Efficient construction of the Feynman-Vernon influence functional as matrix product states
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- Tensor cross interpolation approach for quantum impurity problems based on the weak-coupling expansion
- A comprehensive study of out-of-equilibrium Kondo effect and Coulomb blockade
- Path Integral Formalism for Quantum Open Systems
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- Scalable tensor network algorithm for quantum impurity problems