For the kind of quenches we are studying, the reduced density matrix for the subregion A after the quench can be written as [[rho].sub.A] = [[rho].sup.(0).sub.A] + [[lambda].sub.A][[DELTA].sub.[lambda]][[rho].sub.A] and so can the entanglement entropy:
For quenches of finite duration, it is non-zero only for 0 [less than or equal to] t [less than or equal to] [t.sub.sat].
In this section, we will study the growth of entanglement for small subsystems for some explicit quenches. As we will see, they cover a wide range of time-dependent perturbations to the field theory.
Further, our discussion fills in a gap in the literature [77, 78] for entanglement growth after instantaneous quenches, which has focused more on large subsystems.
Before we study this in detail, we depict in Figure 1 the evolution of entanglement entropy for instantaneous global quenches.
Recall that [t.sub.q] = 0 for instantaneous quenches and hence [t.sub.sat] = [t.sub.*].
This case is more interesting because a Floquet quench that acts for finite duration can be very-well approximated by a finite combination of power-law quenches, whose exact description we know.
In this paper, we studied global quantum quenches to holographic hyperscaling-violating-Lifshitz (hvLif) field theories, using entanglement entropy of a subregion as a probe to study thermalization.
In Section 5, we started studying special examples of global quenches, in particular
It would be interesting to have a more realistic holographic model for studying quenches in hvLif field theories.
Cardy, "Quantum quenches in extended systems," Journal of Statistical Mechanics: Theory and Experiment, no.