Finite-temperature mutual information in a simple phase transition

TL;DR

This paper investigates the behavior of mutual information in the Lipkin-Meshkov-Glick model at finite temperatures, revealing its effectiveness in detecting phase transitions where entanglement measures may fail.

Contribution

It provides exact calculations and numerical evidence showing mutual information diverges at criticality, highlighting its utility over entanglement measures in phase transition detection.

Findings

Mutual information remains finite at non-critical temperatures.

At criticality, mutual information diverges logarithmically with system size.

The divergence's prefactor depends on whether the critical temperature is zero or not.

Abstract

We study the finite-temperature behavior of the Lipkin-Meshkov-Glick model, with a focus on correlation properties as measured by the mutual information. The latter, which quantifies the amount of both classical and quantum correlations, is computed exactly in the two limiting cases of vanishing magnetic field and vanishing temperature. For all other situations, numerical results provide evidence of a finite mutual information at all temperatures except at criticality. There, it diverges as the logarithm of the system size, with a prefactor that can take only two values, depending on whether the critical temperature vanishes or not. Our work provides a simple example in which the mutual information appears as a powerful tool to detect finite-temperature phase transitions, contrary to entanglement measures such as the concurrence.