Dynamics and Thermalisation in Correlated One-Dimensional Lattice Systems

We review exact approaches and recent results related to the relaxation dynamics and description after relaxation of various one-dimensional lattice systems of hard-core bosons after a sudden quench. We first analyse the integrable case, where the combination of analytical insights and computational techniques enable the study of large system sizes. Thermalisation does not occur in this regime. However, after relaxation, observables can be described by a generalisation of the Gibbs ensemble. We then utilise full exact diagonalisation to study what happens as integrability is broken. We show that thermalisation does occur in finite nonintegrable systems provided that they are sufficiently far away from the integrable point. We argue that the onset of thermalisation can be understood in terms of the eigenstate-thermalisation hypothesis.