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

We report results of large-scale Monte Carlo simulations of superfluid-insulator transitions in disordered commensurate 2D bosonic systems. In the off-diagonal disorder case, we find that the transition is to a gapless incompressible insulator, and its dynamical critical exponent is $z=1.5(2)$. In the diagonal-disorder case, we prove the conjecture that rare statistical fluctuations are inseparable from critical fluctuations on the largest scales and ultimately result in 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.

Figure 1

Correlation functions $G(r,0)$ and $G(0,\tau )$ for $K=0.3805,0.3810,0.3815$ and system size $L\times L\times L_{\tau }=160\times 160\times 500$. Error bars are comparable to the linewidths.

Figure 2

Superfluid stiffness of the broken-bond model as a function of $K$ at different system sizes: $40\times 40\times 40$, open circles; $80\times 80\times 80$, filled circles; $160\times 160\times 160$, open squares; $160\times 160\times 500$, filled squares.

Figure 3

Compressibility of the broken-bond model as a function of $K$ at different system sizes: $40\times 40\times 40$, open circles; $80\times 80\times 80$, filled circles; $160\times 160\times 160$, open squares; $160\times 160\times 500$, filled squares.

Figure 4

Superfluid stiffness for the diagonal disorder case as a function of $K$ at different system sizes: $10\times 10\times 20$, filled circles; $20\times 20\times 49$, open circles; $40\times 40\times 121$, filled squares; $80\times 80\times 298$, open squares; $160\times 160\times 733$, triangle down.

Figure 5

Compressibility for the diagonal disorder case as a function of $K$ at different system sizes: $10\times 10\times 20$, filled circles; $20\times 20\times 49$, open circles; $40\times 40\times 121$, filled squares; $80\times 80\times 298$, open squares; $160\times 160\times 733$, triangle down; $160\times 160\times 160$, triangle up. The data for $L\ge 80$ collapse on each other within the error bars.