Exact Treatment of Quantum Quench in a Fermionic System and Time-Dependent Entanglement Entropy

Abstract

We consider a relativistic system of fermions with time-dependent mass, in 1+1 space-time dimensions. We show that the state of this system immediately after a sudden quench, in which the mass is taken to zero, is a generalised Calabrese-Cardy state, as hypothesised earlier. We then proceed to compute the exact post-quench time-dependent propagator and use it to obtain various correlators for a family of pre-quench states, including the ground state and squeezed states. We use these correlators, along with the replica trick and bosonisation methods, to compute the full entanglement entropy of a spatial region. We find that this entropy thermalises as expected.