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

TL;DR

This paper investigates the non-equilibrium dynamics of the Bose-Hubbard model using a projection operator approach, capturing quantum fluctuations beyond mean-field and aligning well with quantum Monte Carlo results and experiments.

Contribution

It introduces a projection operator formalism to study non-equilibrium dynamics of the Bose-Hubbard model, accurately capturing quantum fluctuations beyond mean-field.

Findings

Phase diagram matches quantum Monte Carlo results in 3D

Residual energy, wavefunction overlap, and defect probability do not show universal scaling

Results agree with recent experimental observations

Abstract

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.