Thermalization and Revivals after a Quantum Quench in Conformal Field Theory

We consider a quantum quench in a finite system of length L described by a 1 + 1-dimensional conformal field theory (CFT), of central charge c, from a state with finite energy density corresponding to an inverse temperature beta << L. For times t such that l/2 < t < (L - l)/2 the reduced density matrix of a subsystem of length l is exponentially close to a thermal density matrix. We compute exactly the overlap F of the state at time t with the initial state and show that in general it is exponentially suppressed at large L/beta. However, for minimal models with c < 1 (more generally, rational CFTs), at times which are integer multiples of L/2 (for periodic boundary conditions, L for open boundary conditions) there are (in general, partial) revivals at which F is O(1), leading to an eventual complete revival with F = 1. There is also interesting structure at all rational values of t/L, related to properties of the CFT under modular transformations. At early times t << (L beta)(1/2) there is a universal decay F similar to exp(-(pi c/3)Lt(2)/beta(beta(2) + 4t(2))). The effect of an irrelevant nonintegrable perturbation of the CFT is to progressively broaden each revival at t = nL/2 by an amount O(n(1/2)).