Dynamics of a quantum phase transition in the 1D Bose-Hubbard model: excitations and correlations induced by a quench

TL;DR

This paper investigates the dynamics of quantum phase transitions in the 1D Bose-Hubbard model through numerical simulations of quenches, confirming Kibble-Zurek scaling and analyzing excitation behavior across the transition.

Contribution

It provides the first detailed numerical analysis of quench dynamics in the 1D Bose-Hubbard model, highlighting the role of the Kibble-Zurek mechanism in a Kosterlitz-Thouless transition.

Findings

Scaling behavior consistent with KZM during quenches

No significant excitations in superfluid phase despite gaplessness

Excitations build up after crossing the critical point

Abstract

The ground state of the one-dimensional Bose-Hubbard model at unit filling undergoes the Mott-superfluid quantum phase transition. It belongs to the Kosterlitz-Thouless universality class with an exponential divergence of the correlation length in place of the usual power law. We present numerical simulations of a linear quench both from the Mott insulator to superfluid and back. The results satisfy the scaling hypothesis that follows from the Kibble-Zurek mechanism (KZM). In the superfluid-to-Mott quenches there is no significant excitation in the superfluid phase despite its gaplessness. Since all critical superfluid ground states are qualitatively similar, the excitation begins to build up only after crossing the critical point when the ground state begins to change fundamentally. The last process falls into the KZM framework.