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

TL;DR

This paper proves that in disordered bosonic systems, a direct transition between superfluid and Mott insulator phases cannot occur, and it establishes conditions for the system's compressibility and phase transition boundaries.

Contribution

It introduces a general theorem of inclusions demonstrating the impossibility of direct superfluid-Mott insulator transitions in disordered systems and supports this with quantum Monte Carlo simulations.

Findings

No direct superfluid to Mott insulator transition in disordered systems.

Critical disorder strength exceeds half the Mott gap in the pure system.

Compressibility is maintained on the critical line and nearby regions.

Abstract

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 compressibility of the system on the superfluid--insulator critical line and in its neighborhood. These conclusions follow from a general {\it 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 $\Delta_c > E_{\rm g/2}$, with $E_{\rm g/2}$ the half-width of the Mott gap in the pure system.