Entanglement and mutual information in two-dimensional nonrelativistic field theories

TL;DR

This paper investigates entanglement entropy and mutual information in nonrelativistic conformal field theories using holographic methods, revealing new formulas and structural similarities with flat space cosmologies.

Contribution

It introduces a novel expression for entanglement entropy in (1+1)-dimensional Lifshitz theories at zero and finite temperature, and proposes a conjecture relating to the anomaly coefficient of dual theories.

Findings

Lifshitz entanglement entropy at finite temperature resembles flat space cosmology results.

A new formula for entanglement entropy in Lifshitz theories is derived.

Mutual information behavior in nonrelativistic theories is characterized.

Abstract

We carry out a systematic study of entanglement entropy in nonrelativistic conformal field theories via holographic techniques. After a discussion of recent results concerning Galilean conformal field theories, we deduce a novel expression for the entanglement entropy of (1+1)-dimensional Lifshitz field theories --- this is done both at zero and finite temperature. Based on these results, we pose a conjecture for the anomaly coefficient of a Lifshitz field theory dual to new massive gravity. It is found that the Lifshitz entanglement entropy at finite temperature displays a striking similarity with that corresponding to a flat space cosmology in three dimensions. We claim that this structure is an inherent feature of the entanglement entropy for nonrelativistic conformal field theories. We finish by exploring the behavior of the mutual information for such theories.