Entanglement entropy at higher orders for the states of a = 3 {\theta} = 1 Lifshitz theory

TL;DR

This paper computes higher-order entanglement entropy for a Lifshitz theory with specific parameters, revealing logarithmic and polynomial dependencies on strip width and discussing thermodynamic interpretations.

Contribution

It provides a perturbative calculation of entanglement entropy at second order for a Lifshitz theory with a = 3, θ = 1, including entropy corrections and thermodynamic relations.

Findings

Logarithmic dependence of entropy on strip width at leading order

Entropy of excitations scales as l^4

Entanglement temperature decreases as 1/l^3

Abstract

We evaluate the entanglement entropy of strips for boosted D3-black-branes compactified along the lightcone coordinate. The bulk theory describes $3$-dimensional $a = 3$ ${\theta} = 1$, Lifshitz theory on the boundary. The area of small strips is evaluated perturbatively up to second order, where the leading term has a logarithmic dependence on strip width l, whereas entropy of the excitations is found to be proportional to $l^4$. The entanglement temperature falls off as $\frac{1}{l^3}$ on expected lines. The size of the subsystem has to be bigger than the typical Lifshitz scale in the theory. At second order, the redefinition of temperature(or strip width) is required so as to meaningfully describe the entropy corrections in the form of the first law of entanglement thermodynamics.