# Entanglement in Lifshitz-type Quantum Field Theories

## TL;DR

This paper investigates how quantum entanglement entropy scales in Lifshitz scalar theories, revealing a transition from area law to volume law with increasing dynamical exponent, supported by numerical evidence in multiple dimensions.

## Contribution

It provides the first detailed analysis of entanglement entropy scaling in Lifshitz theories, highlighting the influence of non-local effects and the dynamical exponent.

## Key findings

- Entanglement entropy scales from area law to volume law as dynamical exponent increases.
- Numerical evidence supports the scaling behavior in (1+1) and (2+1) dimensions.
- Corner contributions to entanglement become non-additive at large dynamical exponents.

## Abstract

We study different aspects of quantum entanglement and its measures, including entanglement entropy in the vacuum state of a certain Lifshitz scalar theory. We present simple intuitive arguments based on "non-local" effects of this theory that the scaling of entanglement entropy depends on the dynamical exponent as a characteristic parameter of the theory. The scaling is such that in the massless theory for small entangling regions it leads to area law in the Lorentzian limit and volume law in the $z\to\infty$ limit. We present strong numerical evidences in (1+1) and (2+1)-dimensions in support of this behavior. In (2+1)-dimensions we also study some shape dependent aspects of entanglement. We argue that in the massless limit corner contributions are no more additive for large enough dynamical exponents due to non-local effects of Lifshitz theories. We also comment on possible holographic duals of such theories based on the sign of tripartite information.