Entanglement entropy at higher orders for the states of a = 3 θ = 1 Lifshitz theory

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.