Variational tensor network renormalization in imaginary time: benchmark results in the Hubbard model at finite temperature

TL;DR

This paper introduces a variational tensor network method to efficiently represent the Gibbs operator for 2D lattice systems at finite temperature, enabling accurate simulations of models like the Hubbard model.

Contribution

The paper develops a variational coarse-graining algorithm for tensor networks that accurately constructs finite-temperature operators in 2D lattice models.

Findings

Benchmark results agree with cluster dynamical mean-field theory.

Method accurately captures finite-temperature properties of the Hubbard model.

Algorithm provides a new tool for studying strongly correlated systems.

Abstract

A Gibbs operator $e^{-\beta H}$ for a 2D lattice system with a Hamiltonian $H$ can be represented by a 3D tensor network, the third dimension being the imaginary time (inverse temperature) $\beta$. Coarse-graining the network along $\beta$ results in an accurate 2D projected entangled-pair operator (PEPO) with a finite bond dimension. The coarse-graining is performed by a tree tensor network of isometries that are optimized variationally to maximize the accuracy of the PEPO. The algorithm is applied to the two-dimensional Hubbard model on an infinite square lattice. Benchmark results are obtained that are consistent with the best cluster dynamical mean-field theory and power series expansion in the regime of parameters where they yield mutually consistent results.