Disordered Bosons in One Dimension: From Weak- to Strong-Randomness Criticality

We investigate the superfluid-insulator quantum phase transition of one-dimensional bosons with off-diagonal disorder by means of large-scale Monte Carlo simulations. For weak disorder, we find the transition to be in the same universality class as the superfluid-Mott insulator transition of the clean system. The nature of the transition changes for stronger disorder. Beyond a critical disorder strength, we find nonuniversal, disorder-dependent critical behavior. We compare our results to recent perturbative and strong-disorder renormalization group predictions. We also discuss experimental implications as well as extensions of our results to other systems.

Figure 1

Critical Luttinger parameter $g$ and exponent $\eta$ [plotted as $1/(2\eta )$] of the superfluid-insulator transition as functions of the disorder strength $1-r$. The critical behavior appears universal for weak disorder while it becomes disorder-dependent for strong disorder. The lines are guides to the eye only.

Figure 2

Spatial correlation length ${\xi }_s$ vs. temperature $T$ for disorder strength $r=0.85$ and system sizes $L=200$ to 3200. The solid line is a fit to the KT form (4). Inset: Luttinger parameter $g$ at $T_c$ vs. system size $L$.

Figure 3

Susceptibility $\chi$ vs. temperature $T$ for several disorder strengths. The maximum system sizes are at least $L=1500$. The solid lines are fits to the KT form (5). The resulting estimates of $T_c$ are listed in the legend.

Figure 4

$\ln (\chi /{\xi }_s^2)$ vs. $\ln ({\xi }_s)$ for several disorder strengths and maximum system size $L\ge 1500$ ($L=500$ for $r=0.15$). The solid lines are linear fits; their slopes give $-\eta$.

Figure 5

Susceptibility at $T_c$ plotted as $\ln (\chi /L^2)$ vs. $\ln (L)$ for several disorder strengths. The solid lines are linear fits; their slopes give $-\eta$ (values are shown in Fig. 1). The inset demonstrates the change of slope with increasing $r$.