Lifshitz entanglement entropy from holographic cMERA

TL;DR

This paper investigates holographic entanglement entropy in Lifshitz scalar theories using cMERA-derived geometries, revealing a transition from area to volume law and analyzing effects of mass deformation and RG flow.

Contribution

It introduces a holographic approach to Lifshitz entanglement entropy using cMERA geometries, including analytical results on law transitions and RG flow effects.

Findings

Transition from area to volume law at large z

Mass deformation effects on entanglement entropy in arbitrary dimensions

Monotonic decrease of entanglement entropy along RG flow

Abstract

We study entanglement entropy in free Lifshitz scalar field theories holographically by employing the metrics proposed by Nozaki, Ryu and Takayanagi in \cite{Nozaki:2012zj} obtained from a continuous multi-scale entanglement renormalisation ansatz (cMERA). In these geometries we compute the minimal surface areas governing the entanglement entropy as functions of the dynamical exponent $z$ and we exhibit a transition from an area law to a volume law analytically in the limit of large $z$. We move on to explore the effects of a massive deformation, obtaining results for any $z$ in arbitrary dimension. We then trigger a renormalisation group flow between a Lifshitz theory and a conformal theory and observe a monotonic decrease in entanglement entropy along this flow. We focus on strip regions but also consider a disc in the undeformed theory.