Entanglement after quantum quenches in Lifshitz scalar theories

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, 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.