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

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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/τ with ramp time τ, 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 Δ(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.