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

TL;DR

This paper extends tensor network methods to compute finite-temperature Green functions using METTS and purification, demonstrating efficiency and accuracy comparable to Monte Carlo in impurity models.

Contribution

The authors develop a new tensor network approach for finite-temperature Green functions that improves efficiency and accuracy over existing methods.

Findings

Method is applicable to lattice models and impurity models.

Algorithm achieves results competitive with continuous time Monte Carlo.

Reuse of high-probability METTS enhances computational efficiency.

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.