We prove that previous claims of observing a direct superfluid-Mott insulator transition in the disordered J-current model are in error because numerical simulations were done for too small system sizes and the authors ignored the rigorous theorem.
We study the zero-temperature phase transition of a two-dimensional disordered boson Hubbard model. The phase diagram is constructed in terms of the disorder strength and the chemical potential. Via Monte Carlo simulations, we find a multicritical line separating the weak-disorder regime, where the Mott-insulator-to-superfluid transition occurs, from the strong-disorder regime, where the Bose-glass-to-superfluid transition occurs. On the multicritical line, the insulator-to-superfluid transition has the dynamical critical exponent $z\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}1.35\ifmmode\pm\else\textpm\fi{}0.05$ and the correlation length critical exponent $\ensuremath{\nu}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}0.67\ifmmode\pm\else\textpm\fi{}0.03$. We suggest that the proliferation of the particle-hole pairs screens out the weak-disorder effects.
We review the physics of the Bose–Hubbard model with disorder in the chemical potential focusing on recently published analytical arguments in combination with quantum Monte Carlo simulations. Apart from the superfluid and Mott insulator phases that can occur in this system without disorder, disorder allows for an additional phase, called the Bose glass phase. The topology of the phase diagram is subject to strong theorems proving that the Bose Glass phase must intervene between the superfluid and the Mott insulator and implying a Griffiths transition between the Mott insulator and the Bose glass. The full phase diagrams in 3d and 2d are discussed, and we zoom in on the insensitivity of the transition line between the superfluid and the Bose glass in the close vicinity of the tip of the Mott insulator lobe. We briefly comment on the established and remaining questions in the 1d case, and give a short overview of numerical work on related models.
We investigate the Bose glass phase and the insulator-to-superfluid transition in the two-dimensional disordered Boson Hubbard model in the Villain representation via Monte Carlo simulations. In the Bose glass phase the probability distribution of the local susceptibility is found to have a 1χ2 tail and the imaginary time Green's function decays algebraically C(τ) ≈ τ−1 giving rise to a divergent global susceptibility. By considering the participation ratio it is shown that the excitations in the Bose glass phase are fully localized and a scaling law is established. For commensurate Boson densities we find direct Mott insulator to superfluid transition without an intervening Bose glass phase for weak disorder. For this transition we obtain the critical exponents z = 1, v = 0.7 ± 0.1 and η = 0.1 ± 0.1, which agree with those for the classical three-dimensional XY model without disorder. This indicates that disorder is irrelevant at the tip of the Mott-lobes and that here the inequality v⩾2d is violated.
We use the density-matrix renormalization group to study the one-dimensional bosonic Hubbard model, with and without disorder. We obtain the gaps in all phases, certain correlation functions, and the superfluid density. A finite-size-scaling analysis enables us to obtain an accurate phase diagram and the $\ensuremath{\beta}$ function at the superfluid--Mott insulator transition and the Kosterlitz-Thouless essential singularity in the pure case. We also obtain coupling constants used in effective field theories for this system.