Abstract
Recent experiments with ultracold atoms in an optical lattice have realized cavity-mediated long-range interaction and observed the emergence of a supersolid phase and a density wave phase in addition to Mott insulator and superfluid phases. Here we consider theoretically the effect of uncorrelated disorder on the phase diagram of this system and study the two-dimensional Bose-Hubbard model with cavity-mediated long-range interactions and uncorrelated diagonal disorder. We also study the phase diagram of the extended Bose-Hubbard model with nearest-neighbor interactions in the presence of uncorrelated diagonal disorder. The extended Bose-Hubbard model with nearest-neighbor interactions has been realized in the experiment using dipolar interaction recently. With the help of quantum Monte Carlo simulations using the worm algorithm, we determine the phase diagram of those two models. We compare the phase diagrams of cavity-mediated long-range interactions with nearest-neighbor interactions. We show that two kinds of Bose glass phases exist: one with and one without density wave order. We also find that weak disorder enhances the supersolid phase.Graphical abstract
Highlights
The interplay between disorder and interaction attracts a lot of attention in condensed matter and statistical physics
On the mean-field level the Bose-Hubbard model (BHM) with cavity-mediated interactions is identical to the BHM with nearest-neighbor repulsion – up to a renormalization of the chemical potential and the on-site potential [33]
Comparing the phase diagrams of model (1) and (2), we can see that the phase diagrams of the extended BHM with cavity-mediated long-range interactions and nearest-neighbor interactions only vaguely similar and display many significant differences
Summary
The interplay between disorder and interaction attracts a lot of attention in condensed matter and statistical physics. The so-called extended BHM includes nearest-neighbor and/or long-range interactions, as for instance dipolar interactions and cavity-mediated interactions. The study of the extended BHM with cavity-mediated long-range interactions in the presence of disorder is still lacking. We use quantum Monte Carlo simulations based on the worm algorithm [46] to study the phase diagram of the two-dimensional Bose-Hubbard model with cavity-mediated long-range interactions and uncorrelated disorder. For each Unn/t, Us/t, and ∆/t, we average over 500–1000 realizations of disorder
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