Variational Approach to Projected Entangled Pair States at Finite Temperature

TL;DR

This paper introduces a variational algorithm for optimizing projected entangled pair states (PEPS) at finite temperature, accurately representing thermal states in strongly correlated systems, with demonstrated benchmarks in the quantum Ising model.

Contribution

It presents a novel variational method that accounts for the full tensor environment, enabling PEPS to precisely approximate Gibbs states as bond dimension increases.

Findings

Accurately reproduces Gibbs states in quantum Ising model

Generalizes from 1D MPS to 2D PEPS

Demonstrates convergence with increasing bond dimension

Abstract

The projected entangled pair state (PEPS) ansatz can represent a thermal state in a strongly correlated system. We introduce a novel variational algorithm to optimize this tensor network. Since full tensor environment is taken into account, then with increasing bond dimension the optimized PEPS becomes the exact Gibbs state. Our presentation opens with a 1D version for a matrix product state (MPS) and then generalizes to PEPS in 2D. Benchmark results in the quantum Ising model are presented.