# Entanglement after Quantum Quenches in Lifshitz Scalar Theories

## TL;DR

This paper investigates how entanglement entropy evolves after quantum quenches in Lifshitz scalar theories with dynamical exponent z>1, revealing delayed critical times and long-range interaction effects.

## Contribution

It provides a detailed analysis of entanglement dynamics in Lifshitz theories, highlighting the delayed critical time for z>1 and the interplay of fast and slow quasiparticles.

## Key findings

- Critical time t_c is delayed for z>1 due to quasiparticle competition.
- Entanglement entropy increases with z, indicating long-range interactions.
- Late-time entanglement behavior differs between ECP and CCP protocols.

## Abstract

We study the time evolution of the entanglement entropy after quantum quenches in Lifshitz free scalar theories, with the dynamical exponent $z>1$, by using the correlator method. For quantum quenches we consider two types of time-dependent mass functions: end-critical-protocol (ECP) and cis-critical-protocol (CCP). In both cases, at early times the entanglement entropy is independent of the subsystem size. After a critical time ($t_c$), the entanglement entropy starts depending on the subsystem size significantly. This critical time $t_c$ for $z = 1$ in the fast ECP and CCP has been explained well by the fast quasi-particle of the quasi-particle picture. However, we find that for $z > 1$ this explanation does not work and $t_c$ is delayed. We explain why $t_c$ is delayed for $z>1$ based on the quasiparticle picture: in essence, it is due to the competition between the fast and slow quasiparticles. At late times, in the ECP, the entanglement entropy slowly increases while, in the CCP, it is oscillating with a well defined period by the final mass scale, independently of $z$. We give an interpretation of this phenomena by the correlator method. As $z$ increases, the entanglement entropy increases, which can be understood by long-range interactions due to $z$.