Disentangling the Thermofield-double state

Abstract

In this note we will study the evolution of the thermofield-double state under a quantum quench made by double traced operators in the context of SYK model. We will compute the entanglement entropy of the resulting state to second order in the coupling using the replica method. The entanglement entropy will increase (decrease) depending on the sign of the coupling. We will also compute the two point function to leading order. The system will thermalize again after a time of order t ∼ β/2pΔ with a new temperature, where p and Δ are the number of left and right Majorana fermions in the interaction hamiltonian and the scaling dimension of the Majorana fermions, respectively. From bulk point of view the decrease (increase) in entanglement entropy corresponds to the shrinking (expansion) of the black hole's event horizon.