A large scale exact diagonalization study of thermalization in a non-integrable quantum spin chain

Using a Krylov-subspace time evolution algorithm, we simulate the real-time dynamics of non-integrable finite spin rings to quite long times with high accuracy. We systematically study the finite-size deviation between the resulting equilibrium state and the thermal state, and we highlight the importance of the energy variance on the deviations. We find that the deviations are well described by the eigenstate thermalization hypothesis, and that the von Neumann entropy deviation scaling is the square of the local operator scaling. We also find that local observables relax towards equilibrium exponentially with a time scale that grows linearly with system length and is somewhat independent of the local operator.