The relaxation of closed quantum systems to equilibrium has attracted a lot of interest recently. Besides being a question of fundamental interest connected to the validity of statistical mechanics, recent experimental advances made it possible to study these phenomena in the lab. Some exotic observations are thought to be explained by integrability of the quantum system. It was suggested that for integrable quantum systems the relaxation leads to a generalized Gibbs ensemble instead of a thermal state. In this talk I review these issues for the non-specialists, and present the results of a study of the nonequilibrium time evolution of the spin-1/2 anisotropic Heisenberg (XXZ) spin chain, with the conclusion that the GGE cannot give a complete description even of local observables. On the other hand, an alternative approach known as the quench-action formalism correctly captures the steady state. I also discuss the mechanism of, and possible remedies for, the failure of the GGE.

Joint seminar of MTA-DE (Hungarian Academy of Sciences - University of Debrecen) Particle Physics Research Group and of MTA Atomki Momentum Research Group on Lattice-QCD.