Non-equilibrium dynamics of the Bose-Hubbard model: A projection operator approach

We study the phase diagram and non-equilibrium dynamics, both subsequent to a sudden quench of the hopping amplitude $J$ and during a ramp $J(t)=Jt/\tau$ with ramp time $\tau$, of the Bose-Hubbard model at zero temperature using a projection operator formalism which allows us to incorporate the effects of quantum fluctuations beyond mean-field approximations in the strong coupling regime. Our formalism yields a phase diagram which provides a near exact match with quantum Monte Carlo results in three dimensions. We also compute the residual energy $Q$, the superfluid order parameter $\Delta(t)$, the equal-time order parameter correlation function $C(t)$, and the wavefunction overlap $F$ which yields the defect formation probability $P$ during non-equilibrium dynamics of the model. We find that $Q$, $F$, and $P$ do not exhibit the expected universal scaling. We explain this absence of universality and show that our results compare well with recent experiments.