Quantum Belief Propagation

TL;DR

Quantum belief propagation (QBP) is a numerical algorithm for simulating one-dimensional quantum systems at non-zero temperature, leveraging short-range quantum effects to achieve high accuracy with minimal computational effort.

Contribution

The paper introduces QBP, a novel numerical method that efficiently simulates 1D quantum systems at finite temperature by exploiting short-range quantum correlations.

Findings

QBP accurately reproduces peak susceptibility with minimal computational resources

A modest calculation with 10x10 matrices achieves less than 10^{-5} error

More elaborate calculations further improve accuracy

Abstract

We present an accurate numerical algorithm, called quantum belief propagation (QBP), for simulation of one-dimensional quantum systems at non-zero temperature. The algorithm exploits the fact that quantum effects are short-range in these systems at non-zero temperature, decaying on a length scale inversely proportional to the temperature. We compare to exact results on a spin-1/2 Heisenberg chain. Even a very modest calculation, requiring diagonalizing only 10-by-10 matrices, reproduces the peak susceptibility with a relative error of less than $10^{-5}$, while more elaborate calculations further reduce the error.