Abstract
We use quantum Monte Carlo simulations with the worm algorithm to study the phase diagram of a two-dimensional Bose-Hubbard model with cavity-mediated long-range interactions and uncorrelated disorder in the hard-core limit. Our study shows the system is in a supersolid phase at weak disorder and a disordered solid phase at stronger disorder. Due to long-range interactions, a large region of metastable states exists in both clean and disordered systems. By comparing the phase diagrams for both clean and disordered systems, we find that disorder suppresses metastable states and superfluidity. We compare these results with the phase diagram of the extended Bose-Hubbard model with nearest-neighbor interactions. Here, the supersolid phase does not exist even at weak disorder. We identify two kinds of glassy phases: a Bose glass phase and a disordered solid phase. The glassy phases intervene between the density-wave and superfluid phases as the Griffiths phase of the Bose-Hubbard model. The disordered solid phase intervenes between the density-wave and Bose glass phases since both have a finite structure factor.
Highlights
The study of adding disorder to interacting many-body bosonic systems attracts significant attention both experimentally and theoretically [1,2,3,4,5,6,7,8,9,10,11,12,13,14]
In the hard-core limit and without disorder, equilibrium phases of lattice bosons with cavity-mediated long-range interactions were investigated in Iglói et al [46] and Bla et al [47] in 1D; the result showed that the checkerboard supersolid did not exist
Both the disordered solid (DS) phase and the Bose glass (BG) phase are characterized by a finite compressibility, the difference between them is that Disordered solid (DS) phase has a finite structure factor
Summary
The study of adding disorder to interacting many-body bosonic systems attracts significant attention both experimentally and theoretically [1,2,3,4,5,6,7,8,9,10,11,12,13,14]. Ultracold atoms in optical lattices are a promising tool to study quantum phases and quantum phase transitions in strongly correlated quantum many-body systems. In the hard-core limit and without disorder, equilibrium phases of lattice bosons with cavity-mediated long-range interactions were investigated in Iglói et al [46] and Bla et al [47] in 1D; the result showed that the checkerboard supersolid did not exist. The paper is organized as follows: in section 2, we introduce the Hamiltonian of the system of hard-core bosons with cavity-mediated longrange and nearest-neighbor interactions in the presence of disorder.
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