Anomalous quantum glass of bosons in a random potential in two dimensions

TL;DR

This study uses quantum Monte Carlo simulations to explore the properties of the anomalous Bose glass phase in a 2D disordered Bose-Hubbard model, revealing distinct glass states with different compressibility behaviors.

Contribution

It identifies and characterizes two distinct types of Bose glass states in the 2D Bose-Hubbard model with disorder, highlighting a phase transition or sharp crossover between them.

Findings

The anomalous Bose glass exhibits an exponential temperature dependence of compressibility with a small or vanishing offset.

A conventional Bose glass at stronger disorder is highly compressible.

Small changes in disorder strength can drastically alter the low-temperature compressibility.

Abstract

We present a quantum Monte Carlo study of the "quantum glass" phase of the 2D Bose-Hubbard model with random potentials at filling $\rho=1$. In the narrow region between the Mott and superfluid phases the compressibility has the form $\kappa \sim {\rm exp}(-b/T^\alpha)+c$ with $\alpha <1$ and $c$ vanishing or very small. Thus, at $T=0$ the system is either incompressible (a Mott glass) or nearly incompressible (a Mott-glass-like anomalous Bose glass). At stronger disorder, where a glass reappears from the superfluid, we find a conventional highly compressible Bose glass. On a path connecting these states, away from the superfluid at larger Hubbard repulsion, a change of the disorder strength by only $10\%$ changes the low-temperature compressibility by more than four orders of magnitude, lending support to two types of glass states separated by a phase transition or a sharp cross-over.