Dynamics of the Mott Insulator to Superfluid quantum phase transition in the truncated Wigner approximation

TL;DR

This paper investigates the dynamics of the Mott insulator to superfluid quantum phase transition in the Bose-Hubbard model across different dimensions using the truncated Wigner approximation, confirming the Kibble-Zurek scenario.

Contribution

It provides a detailed analysis of the transition dynamics in multiple dimensions and confirms the power-law scaling and Kibble-Zurek mechanism through numerical simulations.

Findings

Energy scales as a power law with transition rate, exponent approximately 1/3.

Results agree with experimental observations and previous numerical studies.

Confirms the applicability of the Kibble-Zurek scenario to this quantum phase transition.

Abstract

The quantum phase transition from the Mott insulator state to the superfluid in the Bose-Hubbard model is investigated. We research one, two and three dimensional lattices in the truncated Wigner approximation. We compute both kinetic and potential energy and they turn out to have a power law behaviour as a function of the transition rate, with the power equal to 1/3. The same applies to the total energy in a system with a harmonic trap, which is usually present in the experimental set-up. These observations are in agreement with the experiment of [8], where such scalings were also observed and the power of the decay was numerically close to 1/3. The results confirm the Kibble-Zurek (adiabatic-impulse-adiabatic approximation) scenario for this transition.