  In this work, we study the quench dynamics of quantum phases of ultracold
neutral bosons trapped in optical lattices. We investigate the validity of the
Kibble-Zurek (KZ) scaling laws with the single-site Gutzwiller mean-field
(SGMF) and cluster Gutzwiller mean-field (CGMF) theory. With CGMF, we note the
evolution of the dynamical wavefunction in the ``impulse" regime of the
Kibble-Zurek mechanism. We obtain the power law scalings for the crossover time
and defect density with the quench rate predicted by KZ scaling laws. The
critical exponents obtained from dynamics are close to their equilibrium
values. Furthermore, it is observed that the obtained dynamical critical
exponent $z$ improves towards the equilibrium value with increasing cluster
sizes in CGMF.
