Quenches in quantum many-body systems: One-dimensional Bose-Hubbard model reexamined

When a quantum many-body system undergoes a quench, the time-averaged density-matrix $\rho$ governs the time-averaged expectation value of any observable. It is therefore the key object to look at when comparing results with equilibrium predictions. We show that the weights of $\rho$ can be efficiently computed with Lanczos diagonalization for relatively large Hilbert spaces. As an application, we investigate the crossover from perturbative to non-perturbative quenches in the non-integrable Bose-Hubbard model: on finite systems, an approximate Boltzmann distribution is observed for small quenches, while for larger ones the distributions do not follow standard equilibrium predictions. Studying thermodynamical features, such as the energy fluctuations and the entropy, shows that $\rho$ bears a memory of the initial state.