Scalable tensor network algorithm for thermal quantum many-body systems in two dimension

TL;DR

This paper introduces a scalable tensor network algorithm for simulating finite-temperature properties of two-dimensional quantum many-body systems, enabling more efficient and accurate computations in strongly correlated physics.

Contribution

The authors develop a novel finite-temperature tensor network method using PEPS and stochastic reconfiguration, advancing the simulation capabilities for 2D quantum systems at finite temperatures.

Findings

Accurately reproduces thermodynamic properties of 2D models

Benchmarked against SSE, exact diagonalization, and DQMC results

Demonstrates scalability and effectiveness for complex quantum systems

Abstract

Simulating strongly-correlated quantum many-body systems at finite temperatures is a significant challenge in computational physics. In this work, we present a scalable finite-temperature tensor network algorithm for two-dimensional quantum many-body systems. We employ the (fermionic) projected entangled pair state (PEPS) to represent the vectorization of the quantum thermal state and utilize a stochastic reconfiguration method to cool down the quantum states from infinite temperature. We validate our method by benchmarking it against the 2D antiferromagnetic Heisenberg model, the $J_1$-$J_2$ model, and the Fermi-Hubbard model, comparing physical properties such as internal energy, specific heat, and magnetic susceptibility with results obtained from stochastic series expansion (SSE), exact diagonalization, and determinant quantum Monte Carlo (DQMC).