Paper detail

Entanglement after Quantum Quenches in Lifshitz Scalar Theories

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 $z$.