Superfluid--Insulator Transition in Commensurate Disordered Bosonic Systems:Large-Scale Worm-Algorithm Simulations

TL;DR

This study uses large-scale Monte Carlo simulations to analyze superfluid-insulator transitions in 2D disordered bosonic systems, revealing distinct critical behaviors depending on the type of disorder and explaining previous conflicting results.

Contribution

It provides the first large-scale simulation evidence for different universality classes of the transition under diagonal and off-diagonal disorder in 2D bosonic systems.

Findings

Transition to a gapless incompressible insulator with z≈1.65 under off-diagonal disorder.

Crossover to a universal class with z≈2 under diagonal disorder at large scales.

Universal behavior emerges only at very large space-time distances, clarifying previous smaller-scale studies.

Abstract

We report results of large-scale Monte Carlo simulations of superfluid--insulator transitions in commensurate 2D bosonic systems. In the case of off-diagonal disorder (quantum percolation), we find that the transition is to a gapless incompressible insulator, and its dynamical critical exponent is $z=1.65 \pm 0.2$. In the case of diagonal disorder, we prove the conjecture that rare statistical fluctuations are inseparable from critical fluctuations on the largest scales and ultimately result in the crossover to the generic universality class (apparently with $z=2$). However, even at strong disorder, the universal behavior sets in only at very large space-time distances. This explains why previous studies of smaller clusters mimicked a direct superfluid--Mott-insulator transition.