Mixed State Entanglement and Thermal Phase Transitions

TL;DR

This paper investigates how holographic entanglement measures like HEE, MI, and EoP can diagnose superconducting phase transitions, revealing their distinct behaviors and the richer information EoP provides.

Contribution

The study demonstrates the diagnostic power of holographic entanglement measures at phase transitions and introduces a new algorithm for computing EoP in general configurations.

Findings

HEE, MI, and EoP are continuous at the critical point but have discontinuous first derivatives.

MI decreases and is convex with temperature, while HEE increases and is concave.

EoP can behave similarly or oppositely to MI, depending on configuration size.

Abstract

We study the relationship between mixed state entanglement and thermal phase transitions. As a typical example, we compute the holographic entanglement entropy (HEE), holographic mutual information (MI) and the holographic entanglement of purification (EoP) over the superconductivity phase transition. We find that HEE, MI and EoP can all diagnose the superconducting phase transition. They are continuous at the critical point, but their first derivative with respect to temperature is discontinuous. MI decreases with increasing temperature and exhibits a convex behavior, while HEE increases with increasing temperature and exhibits a concave behavior. However, EoP can exhibit either the same or the opposite behavior as MI, depending on the size of the specific configuration. These results show that EoP captures more abundant information than HEE and MI. We also provide a new algorithm to compute the EoP for general configurations.