Grassmann Time-Evolving Matrix Product Operators for Equilibrium Quantum Impurity Problems

Abstract

Tensor-network-based methods are promising candidates to solve quantum impurity problems. They are free of sampling noises and the sign problem compared to state-of-the-art continuous-time quantum Monte Carlo methods. Recent progress made in tensor-network-based impurity solvers is to use the Feynman-Vernon influence functional to integrate out the bath analytically, retaining only the impurity dynamics and representing it compactly as a matrix product state. The recently proposed Grassmann time-evolving matrix product operator (GTEMPO) method is one of the representative methods in this direction. In this work, we systematically study the performance of GTEMPO in solving equilibrium quantum impurity problems at a finite temperature with a semicircular spectrum density of the bath. Our results show that its computational cost would generally increase as the temperature goes down and scale exponentially with the number of orbitals. In particular, the single-orbital Anderson impurity model can be efficiently solved with this method, for two orbitals we estimate that one could possibly reach inverse temperature $\beta \approx 20$ if high-performance computing techniques are utilized, while beyond that only very high-temperature regimes can be reached in the current formalism. Our work paves the way to apply GTEMPO as an imaginary-time impurity solver.

12 pages, 10 figures

References in corpus (14)

• The density-matrix renormalization group in the age of matrix product 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
• Strong electronic correlations from Hund's coupling
• Continuous-time auxiliary field Monte Carlo for quantum impurity models
• Solving nonequilibrium dynamical mean-field theory using matrix product states
• Chebyshev Matrix Product State Impurity Solver for the Dynamical Mean-Field Theory
• Metal-Insulator phase diagram and orbital selectivity in 3-orbital models with rotationally invariant Hund coupling
• Chebyshev expansion for Impurity Models using Matrix Product States
• The Hidden Phase of the Spin-Boson Model
• Grassmann Time-Evolving Matrix Product Operators for Quantum Impurity Models
• Equilibrium Quantum Impurity Problems via Matrix Product State Encoding of the Retarded Action
• Hubbard-Kanamori model: spectral functions, negative electron compressibility, and susceptibilities

Cited by in corpus (7)

• Real-time Impurity Solver Using Grassmann Time-Evolving Matrix Product Operators
• Infinite Grassmann Time-Evolving Matrix Product Operator Method in the Steady State
• Solving quantum impurity problems on the L-shaped Kadanoff-Baym contour
• Efficient construction of the Feynman-Vernon influence functional as matrix product states
• 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
• Scalable tensor network algorithm for quantum impurity problems