Quench dynamics across the MI-SF quantum phase transition with cluster mean field theory

TL;DR

This paper investigates the quench dynamics of ultracold bosons across the MI-SF transition using cluster mean-field theory, confirming Kibble-Zurek scaling laws and showing improved critical exponents with larger clusters.

Contribution

It introduces the use of cluster Gutzwiller mean-field theory to analyze quench dynamics and validates Kibble-Zurek scaling laws with improved accuracy for critical exponents.

Findings

Power law scaling for crossover time and defect density with quench rate.

Critical exponents from dynamics are close to equilibrium values.

Dynamical critical exponent $z$ improves with larger cluster sizes.

Abstract

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.