The quasi-particle gap in a disordered boson Hubbard model in two dimensions

TL;DR

This study uses Monte Carlo simulations to analyze how the quasi-particle energy gap behaves near quantum phase transitions in a disordered two-dimensional boson Hubbard model, revealing conditions for Mott insulator, superfluid, and Bose glass phases.

Contribution

It provides detailed numerical evidence on the nature of phase transitions and the role of disorder strength in the boson Hubbard model.

Findings

Gapped Mott insulator persists up to the transition with weak disorder.

Bose glass phase appears only beyond a critical disorder strength.

Direct Mott-insulator-to-superfluid transition is supported under certain conditions.

Abstract

We investigate the behavior of the quasi-particle energy gap near quantum phase transitions in a two-dimensional disordered boson Hubbard model at a commensurate filling. Via Monte Carlo simulations of ensembles with fixed numbers of particles, we observe the behavior of the gap as a function of the tuning parameter for various strength of diagonal disorder. For weak disorder, we find that gapped Mott insulating phase is sustained up to the transition point and disappears only in a superfluid, strongly supporting a direct Mott-insulator-to-superfluid transition. Bose glass behavior, insulating with vanishing gap, appears only when the strength of disorder is bigger than a critical value.