Entanglement thermodynamics for an excited state of Lifshitz system

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.

12 pages, no figure; v2: some typos fixed, few references added

References in corpus (3)

• Thermodynamical Property of Entanglement Entropy for Excited States
• Holographic stress tensor for non-relativistic theories
• Holographic Entanglement Entropy of Multiple Strips

Cited by in corpus (6)

• Holographic entanglement entropy in the nonconformal medium
• Informational properties of holographic Lifshitz field theory
• Entanglement entropy and the first law at third order for boosted black branes
• Information theoretic measures for Lifshitz system
• More on entanglement properties of $Li{f}_4^{(2)}\times S^1\times S^5$ spacetime with string excitations
• HEE and HSC for flavors: perturbative structure in open string geometries