Infinite Grassmann time-evolving matrix product operator method for zero-temperature equilibrium quantum impurity problems
arXiv:2404.04757 · doi:10.1103/PhysRevB.110.165119
Abstract
The Grassmann time-evolving matrix product operator (GTEMPO) method has proven to be an accurate and efficient numerical method for the real-time dynamics of quantum impurity problems. Whereas its application for imaginary-time calculations is much less competitive compared to well-established methods such as the continuous-time quantum Monte Carlo (CTQMC). In this work, we unleash the full power of GTEMPO for zero-temperature imaginary-time calculations: the multi-time impurity state is time-translationally invariant with infinite boundary condition, therefore it can be represented as an infinite Grassmann matrix product state (GMPS) with nontrivial unit cell in a single time step, instead of an open boundary GMPS spanning the whole imaginary-time axis. We devise a very efficient infinite GTEMPO algorithm targeted at zero-temperature equilibrium quantum impurity problems, which is known to be a hard regime for quantum Monte Carlo methods. To demonstrate the performance of our method, we benchmark it against exact solutions in the noninteracting limit, and against CTQMC calculations in the Anderson impurity models with up to two orbitals, where we show that the required bond dimension of the infinite GMPS is much smaller than its finite-temperature counterpart.
arXiv comment9 pages, 7 figures
References in corpus (61)
- A Practical Introduction to Tensor Networks: Matrix Product States and Projected Entangled Pair States
- Continuous-time Monte Carlo methods for quantum impurity models
- The numerical renormalization group method for quantum impurity systems
- Computational complexity and fundamental limitations to fermionic quantum Monte Carlo simulations
- A continuous-time solver for quantum impurity models
- Continuous Time Quantum Monte Carlo method for fermions
- The iTEBD algorithm beyond unitary evolution
- TRIQS: A Toolbox for Research on Interacting Quantum Systems
- 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
- Keldysh technique and non-linear sigma-model: basic principles and applications
- Time-evolving a matrix product state with long-ranged interactions
- Zero temperature metal-insulator transition in the infinite-dimensional Hubbard model
- TRIQS/CTHYB: A Continuous-Time Quantum Monte Carlo Hybridization Expansion Solver for Quantum Impurity Problems
- Energy resolution and discretization artefacts in the numerical renormalization group
- Variational optimization algorithms for uniform matrix product states
- Continuous-time auxiliary field Monte Carlo for quantum impurity models
- How bad metals turn good: spectroscopic signatures of resilient quasiparticles
- Efficient real frequency solver for dynamical mean field theory
- Exploiting the causal tensor network structure of quantum processes to efficiently simulate non-Markovian path integrals
- 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
- Sum-rules and bath-parametrization for quantum cluster theories
- Chebyshev Matrix Product State Impurity Solver for the Dynamical Mean-Field Theory
- Exponential Thermal Tensor Network Approach for Quantum Lattice Models
- Fork Tensor Product States - Efficient Three Orbital Real Time DMFT Solver
- Chebyshev expansion for Impurity Models using Matrix Product States
- Efficient exploration of Hamiltonian parameter space for optimal control of non-Markovian open quantum systems
- Efficient DMFT impurity solver using real-time dynamics with Matrix Product States
- Exact dynamics of non-additive environments in non-Markovian open quantum systems
- Imaginary-time matrix product state impurity solver for dynamical mean-field theory
- An efficient method for quantum impurity problems out of equilibrium
- Quantum heat statistics with time-evolving matrix product operators
- 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
- Using the Environment to Understand non-Markovian Open Quantum Systems
- Quantum Renormalization Groups Based on Natural Orbitals
- Adaptive broadening to improve spectral resolution in the numerical renormalization group
- A partial fraction decomposition of the Fermi function
- 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
- The Hidden Phase of the Spin-Boson Model
- 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
- Configuration interaction based nonequilibrium steady state impurity solver
- Natural-Orbital Impurity Solver and Projection Approach for Green's Function
- Grassmann Time-Evolving Matrix Product Operators for Quantum Impurity Models
- Natural Orbitals Renormalization Group Approach to the Two-Impurity Kondo Critical Point
- Continuous matrix product operator approach to finite temperature quantum states
- Equilibrium Quantum Impurity Problems via Matrix Product State Encoding of the Retarded Action
- Tensor network influence functionals in the continuous-time limit: connections to quantum embedding, bath discretization, and higher-order time propagation
- Heat Current in Non-Markovian Open Systems
- Grassmann Time-Evolving Matrix Product Operators for Equilibrium Quantum Impurity Problems
- Real-time Impurity Solver Using Grassmann Time-Evolving Matrix Product Operators
- Hubbard-Kanamori model: spectral functions, negative electron compressibility, and susceptibilities
- Infinite Grassmann Time-Evolving Matrix Product Operator Method in the Steady State
- Efficient construction of the Feynman-Vernon influence functional as matrix product states