Minimally Entangled Typical Thermal States Algorithms for Finite Temperature Matsubara Green Functions

Abstract

We extend finite-temperature tensor network methods to compute Matsubara imaginary-time correlation functions, building on the minimally entangled typical thermal states (METTS) and purification algorithms. While imaginary-time correlation functions are straightforward to formulate with these methods, care is needed to avoid convergence issues that would result from naive estimators. As a benchmark, we study the single-band Anderson impurity model, even though the algorithm is quite general and applies to lattice models. The special structure of the impurity model benchmark system and our choice of basis enable techniques such as reuse of high-probability METTS for increasing algorithm efficiency. The results are competitive with state-of-the-art continuous time Monte Carlo. We discuss the behavior of computation time and error as a function of the number of purified sites in the Hamiltonian.

12 pages, 11 figures

References in corpus (15)

• 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
• Matrix Product Density Operators: Simulation of finite-T and dissipative systems
• Minimally Entangled Typical Thermal State Algorithms
• Continuous-time auxiliary field Monte Carlo for quantum impurity models
• Time Dependent Variational Principle with Ancillary Krylov Subspace
• Solving nonequilibrium dynamical mean-field theory using matrix product states
• Mott insulating states with competing orders in the triangular lattice Hubbard model
• Chebyshev Matrix Product State Impurity Solver for the Dynamical Mean-Field Theory
• Quantum Monte-Carlo for correlated out-of-equilibrium nanoelectronics devices
• Spectral functions and time evolution from the Chebyshev recursion
• Electron spectra close to a metal-to-insulator transition
• Quantum Monte Carlo solution of the dynamical mean field equations in real time
• Quantum Quasi-Monte Carlo algorithm for out-of-equilibrium Green functions at long times

Cited by in corpus (3)

• Equilibrium Quantum Impurity Problems via Matrix Product State Encoding of the Retarded Action
• Time-dependent ghost-Gutzwiller non-equilibrium dynamics
• Finite Temperature Minimal Entangled Typical Thermal States Impurity Solver