Finite Size Scaling of Mutual Information: A Scalable Simulation

TL;DR

This paper introduces a quantum Monte Carlo method to analyze the finite size scaling of mutual information in quantum many-body systems at finite temperature, revealing non-monotonic behavior and critical point corrections.

Contribution

It presents a scalable simulation technique for computing Renyi mutual information in interacting quantum systems at non-zero temperature.

Findings

Mutual information converges to a limiting function as system size increases.

Non-monotonic temperature dependence of mutual information indicates correlation onset.

Finite size corrections are significant near critical points.

Abstract

We develop a quantum Monte Carlo procedure to compute the Renyi mutual information of an interacting quantum many-body system at non-zero temperature. Performing simulations on a spin-1/2 XXZ model, we observe that for a subregion of fixed size embedded in a system of size L, the mutual information converges at large L to a limiting function which displays non-monotonic temperature behavior corresponding to the onset of correlations. For a region of size L/2 embedded in a system of size L, the mutual information divided by L converges to a limiting function of temperature, with apparently nontrivial corrections near critical points.