Holographic entanglement entropy in the nonconformal medium

TL;DR

This paper explores holographic entanglement entropy in a nonconformal medium with a gravity dual, revealing a size-dependent entanglement chemical potential and thermodynamic-like relations for small subsystems.

Contribution

It introduces the concept of entanglement chemical potential with nontrivial size dependence and analyzes entanglement entropy in both grandcanonical and canonical ensembles.

Findings

Entanglement entropy of small subsystems obeys a thermodynamics-like law.

The entanglement chemical potential depends on the subsystem size.

Global quenches cause measurable changes in entanglement entropy.

Abstract

We investigate holographically the entanglement entropy of a nonconformal medium whose dual geometry is described by an Einstein-Maxwell-dilaton theory. Due to an additional conserved charge corresponding to the number operator, its thermodynamics can be represented in a grandcanonical or canonical ensemble. We study thermodynamics in both ensembles by using the holographic renormalization and the entanglement entropy of a nonconformal medium. After defining the entanglement chemical potential which unlike the entanglement temperature has a nontrivial size dependence, we find that the entanglement entropy of a small subsystem satisfies the relation resembling the first law of thermodynamics in a medium. Furthermore, we study the entanglement entropy change in the nonconformal medium caused by the excitation of the ground state and by the global quench corresponding to the insertion of particles.