# Entanglement Entropy in Lifshitz Theories

## TL;DR

This paper analyzes entanglement entropy in (1+1)-dimensional Lifshitz scalar theories, revealing linear growth with the dynamical exponent and a crossover from area to volume law, with implications for a c-theorem.

## Contribution

It provides analytical results on how entanglement entropy scales with the dynamical exponent in Lifshitz theories and explores the behavior under relevant deformations.

## Key findings

- EE grows linearly with the dynamical exponent
- Crossover from area law to volume law as exponent increases
- EE decreases from UV to IR fixed point in deformed theories

## Abstract

We discuss and compute entanglement entropy (EE) in (1+1)-dimensional free Lifshitz scalar field theories with arbitrary dynamical exponents. We consider both the subinterval and periodic sublattices in the discretized theory as subsystems. In both cases, we are able to analytically demonstrate that the EE grows linearly as a function of the dynamical exponent. Furthermore, for the subinterval case, we determine that as the dynamical exponent increases, there is a crossover from an area law to a volume law. Lastly, we deform Lifshitz field theories with certain relevant operators and show that the EE decreases from the ultraviolet to the infrared fixed point, giving evidence for a possible c-theorem for deformed Lifshitz theories.