Finite Temperature Critical Behavior of Mutual Information

TL;DR

This paper investigates the critical behavior of mutual information in interacting quantum systems at finite temperatures, revealing distinct phenomena for different Renyi entropy indices and connecting results to conformal field theory and boundary entropy concepts.

Contribution

It provides a comprehensive analysis of the finite-temperature critical behavior of mutual information for arbitrary Renyi index n, including new scaling insights and exact result connections.

Findings

Critical behavior at two temperatures T_c and n*T_c for n>1

Area-law coefficient exhibits t*ln(t) singularity in the XXZ model

Corner corrections show logarithmic divergence related to conformal field theory

Abstract

We study mutual information for Renyi entropy of arbitrary index n, in interacting quantum systems at finite-temperature critical points, using high-temperature expansion, quantum Monte Carlo simulations and scaling theory. We find that for n>1, the critical behavior is manifest at two temperatures T_c and n*T_c. For the XXZ model with Ising anisotropy, the coefficient of the area-law has a t*ln(t) singularity, whereas the subleading correction from corners has a logarithmic divergence, with a coefficient related to the exact results of Cardy and Peschel. For T<n*T_c there is a constant term associated with broken symmetries that jumps at both T_c and n*T_c, which can be understood in terms of a scaling function analogous to the boundary entropy of Affleck and Ludwig.