Anomalous suppression of the Bose glass at commensurate fillings in the disordered Bose-Hubbard model

TL;DR

This paper investigates how disorder affects the phase transitions in the Bose-Hubbard model, revealing that at certain fillings, the Bose glass phase is suppressed, potentially allowing a direct Mott insulator to superfluid transition.

Contribution

It provides a one-loop renormalization group analysis showing the suppression of the Bose glass at commensurate fillings in disordered Bose-Hubbard models, including correlations relevant to optical lattice experiments.

Findings

Bose glass suppression at commensurate fillings due to vanishing replica mixing disorder

Potential for direct Mott insulator to superfluid transition in disordered systems

Phase diagrams illustrating the stability of phases under various parameters

Abstract

We study the weakly disordered Bose-Hubbard model on a cubic lattice through a one-loop renormalization group analysis of the corresponding effective field theory which is explicitly derived by combining a strong-coupling expansion with a replica average over the disorder. The method is applied not only to generic uncorrelated on-site disorder but also to simultaneous hopping disorder correlated with the differences of adjacent disorder potentials. Such correlations are inherent in fine-grained optical speckle potentials used as a source of disorder in optical lattice experiments. As a result of strong coupling, the strength of the replica mixing disorder vertex, responsible for the emergence of a Bose glass, crucially depends on the chemical potential and the Hubbard repulsion and vanishes to leading order in the disorder at commensurate boson fillings. As a consequence, at such fillings a direct transition between the Mott-insulator and the superfluid in the presence of disorder cannot be excluded on the basis of a one-loop calculation. At incommensurate fillings, at a certain length scale, the Mott insulator will eventually become unstable towards the formation of a Boss glass. Phase diagrams as a function of the microscopic parameters are presented and the finite-size crossover between the Mott-insulating state and the Bose glass is analyzed.