Aspects of Holographic Entanglement at Finite Temperature and Chemical Potential

TL;DR

This paper analyzes how entanglement entropy and mutual information behave at finite temperature and chemical potential in strongly coupled gauge theories using holographic duality, providing analytic expressions and insights into entanglement transitions.

Contribution

It develops systematic expansions for entanglement entropy in holographic models at finite temperature and chemical potential, revealing the dominant bulk regions and defining an effective temperature scale.

Findings

Entanglement entropy is dominated by thermodynamic entropy at high effective temperature.

Mutual information isolates quantum entanglement, subtracting thermodynamic contributions.

Chemical potential reduces quantum entanglement between sub-regions.

Abstract

We investigate the behavior of entanglement entropy at finite temperature and chemical potential for strongly coupled large-N gauge theories in $d$-dimensions ($d\ge 3$) that are dual to Anti-de Sitter-Reissner-Nordstrom geometries in $(d+1)-$dimensions, in the context of gauge-gravity duality. We develop systematic expansions based on the Ryu-Takayanagi prescription that enable us to derive analytic expressions for entanglement entropy and mutual information in different regimes of interest. Consequently, we identify the specific regions of the bulk geometry that contribute most significantly to the entanglement entropy of the boundary theory at different limits. We define a scale, dubbed as the effective temperature, which determines the behavior of entanglement in different regimes. At high effective temperature, entanglement entropy is dominated by the thermodynamic entropy, however, mutual information subtracts out this contribution and measures the actual quantum entanglement. Finally, we study the entanglement/disentanglement transition of mutual information in the presence of chemical potential which shows that the quantum entanglement between two sub-regions decreases with the increase of chemical potential.