Absence of a Direct Superfluid to Mott Insulator Transition in Disordered Bose Systems

We prove the absence of a direct quantum phase transition between a superfluid and a Mott insulator in a bosonic system with generic, bounded disorder. We also prove the compressibility of the system on the superfluid–insulator critical line and in its neighborhood. These conclusions follow from a general theorem of inclusions, which states that for any transition in a disordered system, one can always find rare regions of the competing phase on either side of the transition line. Quantum Monte Carlo simulations for the disordered Bose-Hubbard model show an even stronger result, important for the nature of the Mott insulator to Bose glass phase transition: the critical disorder bound ${\Delta }_c$ corresponding to the onset of disorder-induced superfluidity, satisfies the relation ${\Delta }_c>E_{g/2}$, with $E_{g/2}$ the half-width of the Mott gap in the pure system.

Figure 1

Winding number squared as a function of interaction strength ($U/t$) for $\Delta =5t$ using a scaling analysis with the temporal exponent $\tilde{z}=2$, chosen for numerical convenience (see text). The corresponding pairs of the linear system size and inverse temperature are : $L=4$ and $\beta t=1$, $L=8$ and $\beta t=4$, $L=16$ and $\beta t=16$, $L=24$ and $\beta t=36$, and finally $L=32$ and $\beta t=64$. The values of the chemical potentials were taken from Ref. 38. Inset: The data points are the intersection points of consecutive curves in the main figure. Extrapolating with $(1/L{)}^2$ to the thermodynamic limit yields $(U/t{)}_c=30.57\pm 0.02$ (see text).

Figure 2

Phase diagram of the 3D Bose-Hubbard model with disorder. The $E_{g/2}(U)$ curve is taken from Ref. 38 and is shown here to demonstrate that the condition ${\Delta }_c(U)>E_{g/2}(U)$ is definitely satisfied. It also marks the BG-MI transition boundary according to the conjecture. Error bars are shown, but are smaller than point sizes.