Critical Properties of the Superfluid - Bose Glass Transition in Two Dimensions

TL;DR

This study uses quantum Monte Carlo simulations to analyze the superfluid to Bose glass transition in two-dimensional disordered bosonic systems, determining critical exponents and the nature of the transition.

Contribution

It provides the first detailed finite-size scaling analysis of the 2D SF-BG transition with precise critical exponents and rules out a percolation mechanism.

Findings

Critical disorder strength $W_c=4.80(5)$ identified.

Critical exponents estimated: $z=1.85(15)$, $ u=1.20(12)$, $eta=-0.40(15)$.

Probability distribution of SF response shows scale invariance at criticality.

Abstract

We investigate the superfluid (SF) to Bose glass (BG) quantum phase transition using extensive quantum Monte Carlo simulations of two-dimensional hard-core bosons in a random box potential. $T=0$ critical properties are studied by thorough finite-size scaling of condensate and SF densities, both vanishing at the same critical disorder $W_c=4.80(5)$. Our results give the following estimates for the critical exponents: $z=1.85(15)$, $\nu=1.20(12)$, $\eta=-0.40(15)$. Furthermore, the probability distribution of the SF response $P(\ln\rho_{\rm sf})$ displays striking differences across the transition: while it narrows with increasing system sizes $L$ in the SF phase, it broadens in the BG regime, indicating an absence of self-averaging, and at the critical point $P(\ln\rho_{\rm sf}+z \ln L)$ is scale invariant. Finally, high-precision measurements of the local density rule out a percolation picture for the SF-BG transition.