Entanglement thermodynamics for an excited state of Lifshitz system

TL;DR

This paper explores the holographic entanglement entropy of excited states in Lifshitz systems, revealing a thermodynamics-like relation influenced by a massive vector field in the gravity dual.

Contribution

It introduces a holographic calculation of entanglement entropy for excited Lifshitz states, highlighting the role of a massive vector field in the thermodynamic analogy.

Findings

Entanglement entropy obeys a first law-like energy relation.

Massive vector field contributes an additional term to the energy relation.

Holographic methods effectively describe excited Lifshitz states.

Abstract

A class of (2+1)-dimensional quantum many body system characterized by an anisotropic scaling symmetry (Lifshitz symmetry) near their quantum critical point can be described by a (3+1)-dimensional dual gravity theory with negative cosmological constant along with a massive vector field, where the scaling symmetry is realized by the metric as an isometry. We calculate the entanglement entropy of an excited state of such a system holographically, i.e., from the asymptotic perturbation of the gravity dual using the prescription of Ryu and Takayanagi, when the subsystem is sufficiently small. With suitable identifications, we show that this entanglement entropy satisfies an energy conservation relation analogous to the first law of thermodynamics. The non-trivial massive vector field here plays a crucial role and contributes to an additional term in the energy relation.