Relaxation to GGE after quantum quenches to quadratic Hamiltonians

The generalized Gibbs ensemble (GGE) conjecture concerns the long-time behavior of local observables in thermodynamically large integrable closed quantum systems. It states that, for generic non-equilibrium initial states, local observables relax at late times to stationary values that can be computed using the GGE density matrix, which maximizes the entropy subject to constraints imposed by all local conserved charges of the integrable system.

The GGE conjecture has already been verified in a variety of integrable models, but analytical verifications have been quite involved, even in the simplest case of quenches to translation-invariant free-particle Hamiltonians. Here, we unify, simplify and extend previous results on relaxation to GGE following quenches to arbitrary quadratic Hamiltonians. We show that, in the absence of localization, all connected correlation functions relax as power laws in time; our simple arguments also yield the exponents for these power laws (for massive, massless, and diffusive dynamics). Finally, we propose extensions of our methods to the interacting integrable and non-integrable cases.