Local Density of the Bose Glass Phase

TL;DR

This paper investigates the local density behavior of the Bose glass phase in the disordered Bose-Hubbard model, revealing different transition mechanisms at incommensurate and commensurate fillings, with multifractal and percolation analyses supporting the findings.

Contribution

It provides a detailed analysis of the local density and phase transitions in the Bose-Hubbard model with disorder, highlighting differences between incommensurate and commensurate fillings and introducing multifractal and percolation perspectives.

Findings

Superfluid-Bose glass transition at incommensurate filling occurs around $ ext{Δ}_c \\approx 30t$.

Local density distribution shows skewness and multifractal behavior near the transition.

Mott insulator-Bose glass transition at commensurate filling occurs around $ ext{Δ}_c \\approx 16t$, with Gaussian local density distribution.

Abstract

We study the Bose-Hubbard model in the presence of on-site disorder in the canonical ensemble and conclude that the local density of the Bose glass phase behaves differently at incommensurate filling than it does at commensurate one. Scaling of the superfluid density at incommensurate filling of $\rho=1.1$ and on-site interaction $U=80t$ predicts a superfluid-Bose glass transition at disorder strength of $\Delta_c \approx 30t$. At this filling the local density distribution shows skew behavior with increasing disorder strength. Multifractal analysis also suggests a multifractal behavior resembling that of the Anderson localization. Percolation analysis points to a phase transition of percolating non-integer filled sites around the same value of disorder. Our findings support the scenario of percolating superfluid clusters enhancing Anderson localization near the superfluid-Bose glass transition. On the other hand, the behavior of the commensurate filled system is rather different. Close to the tip of the Mott lobe ($\rho=1, U=22t$) we find a Mott insulator-Bose glass transition at disorder strength of $\Delta_c \approx 16t$. An analysis of the local density distribution shows Gaussian like behavior for a wide range of disorders above and below the transition.