Emergence of coherence in the Mott--superfluid quench of the Bose-Hubbard model

TL;DR

This paper investigates how phase coherence develops during a quench from the Mott insulator to the superfluid phase in the Bose-Hubbard model, revealing the dynamics of coherence spreading and local condensate formation.

Contribution

It introduces a hierarchy of correlations based on a $1/Z$ expansion to analyze the spatial-temporal growth of phase coherence during the quench.

Findings

Off-diagonal long-range order propagates at a constant speed.

Local condensate patches form during the dynamics.

Phase correlator exhibits diffusion-like growth.

Abstract

We study the quench from the Mott to the superfluid phase in the Bose-Hubbard model and investigate the spatial-temporal growth of phase coherence, i.e., phase locking between initially uncorrelated sites. To this end, we establish a hierarchy of correlations via a controlled expansion into inverse powers of the coordination number $1/Z$. It turns out that the off-diagonal long-range order spreads with a constant propagation speed, forming local condensate patches, whereas the phase correlator follows a diffusion-like growth rate.