Nonequilibrium Dynamics of the Bose-Hubbard Model: A Projection-Operator Approach

We study the phase diagram and nonequilibrium dynamics involving ramp of the hopping amplitude 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 wave function overlap F which yields the defect formation probability P during nonequilibrium 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.