  Motivated by recent experiments, we study the relaxation dynamics and
thermalization in the one-dimensional Bose-Hubbard model induced by a global
interaction quench. Specifically, we start from an initial state that has
exactly one boson per site and is the ground state of a system with infinitely
strong repulsive interactions at unit filling. Using exact diagonalization and
the density matrix renormalization group method, we compute the time dependence
of such observables as the multiple occupancy and the momentum distribution
function. Typically, the relaxation to stationary values occurs over just a few
tunneling times. The stationary values are identical to the so-called diagonal
ensemble on the system sizes accessible to our numerical methods and we further
observe that the micro-canonical ensemble describes the steady state of many
observables reasonably well for small and intermediate interaction strength.
The expectation values of observables in the canonical ensemble agree
quantitatively with the time averages obtained from the quench at small
interaction strengths, and qualitatively provide a good description of
steady-state values even in parameter regimes where the micro-canonical
ensemble is not applicable due to finite-size effects. We discuss our numerical
results in the framework of the eigenstate thermalization hypothesis. Moreover,
we also observe that the diagonal and the canonical ensemble are practically
identical for our initial conditions already on the level of their respective
energy distributions for small interaction strengths. Finally, we discuss
implications of our results for the interpretation of a recent sudden expansion
experiment [Phys. Rev. Lett. 110, 205301 (2013)], in which the same interaction
quench was realized.
