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.

arXiv comment12 pages, no figure; v2: some typos fixed, few references added

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• On the Shape Dependence of Entanglement Entropy
• Holographic complexity for Lifshitz system
• Time-evolution of holographic entanglement entropy and metric perturbations
• Holographic entanglement entropy and generalized entanglement temperature
• Holographic Entanglement Entropy, Subregion Complexity and Fisher Information metric of `black' Non-SUSY D3 Brane
• Entanglement entropy and the first law at third order for boosted black branes
• Entanglement temperature for black branes with hyperscaling violation
• Holographic information theoretic quantities for Lifshitz black hole
• More on entanglement properties of $Li{f}_4^{(2)}\times S^1\times S^5$ spacetime with string excitations
• Information theoretic measures for Lifshitz system
• Holographic complexity of black non-susy D3-brane and the high temperature limit
• HEE and HSC for flavors: perturbative structure in open string geometries
• Entanglement rules for holographic Fermi surfaces