We report on results of Quantum Monte Carlo simulations for bosons in a two dimensional quasiperiodic optical lattice. We study the ground state phase diagram at unity filling and confirm the existence of three phases: superfluid, Mott insulator, and Bose glass. At lower interaction strength, we find that sizable disorder strength is needed in order to destroy superfluidity in favor of the Bose glass. On the other hand, at large enough interaction superfluidity is completely destroyed in favor of the Mott insulator (at lower disorder strength) or the Bose glass (at larger disorder strength). At intermediate interactions, the system undergoes an insulator to superfluid transition upon increasing the disorder, while a further increase of disorder strength drives the superfluid to Bose glass phase transition. While we are not able to discern between the Mott insulator and the Bose glass at intermediate interactions, we study the transition between these two phases at larger interaction strength and, unlike what reported in [1] for random disorder, find no evidence of a Mott-glass-like behavior.Introduction: Condensed matter systems, either manufactured or occurring in nature, posses, in general, a certain degree of disorder. Studying physical phenomena such as Anderson [2] localization, resulting from the presence of disorder, is therefore of crucial importance. Anderson localization pertains to the case of non-interacting fermions. More realistic systems, though, consist of interacting particles. For interacting systems, the interplay between disorder and interaction may result in novel physical effects. For instance, when random disorder is added to paradigmatic condensed matter models, such as the Bose-Hubbard model or the BCS model for superconductivity, it gives rise to disorder-driven phase transitions from a conducting to an insulating phase, resulting from the localization of bosons and cooper pairs, respectively [3][4][5][6]. While disorder driven phase transitions have been observed in a wide range of experimental systems such as films of adsorbed 4 He on substrates [7,8], bosonic magnets [9][10][11], and thin superconducting films [12,13], and in spite of a remarkable theoretical effort [14][15][16][17][18][19][20][21], a thorough understanding of the effects of disorder in interacting quantum many body systems is lacking. On the one hand these systems are challenging to study theoretically, on the other poor control over experimental condensed matter systems does not allow for thorough experimental investigation of these systems.
Ultracold gases offer an unprecedented opportunity to engineer disorder and interactions in a controlled manner. In an effort to understand the interplay between disorder, dipolar interaction and quantum degeneracy, we study two-dimensional hard-core dipolar lattice bosons in the presence of on-site bound disorder. Our results are based on large-scale path-integral quantum Monte Carlo simulations by the Worm algorithm. We study the ground state phase diagram at fixed half-integer filling factor for which the clean system is either a superfluid at lower dipolar interaction strength or a checkerboard solid at larger dipolar interaction strength. We find that, even for weak dipolar interaction, superfluidity is destroyed in favor of a Bose glass at relatively low disorder strength. Interestingly, in the presence of disorder, superfluidity persists for values of dipolar interaction strength for which the clean system is a checkerboard solid. At fixed disorder strength, as the dipolar interaction is increased, superfluidity is destroyed in favor of a Bose glass. As the interaction is further increased, the system eventually develops extended checkerboard patterns in the density distribution. Due to the presence of disorder, though, grain boundaries and defects, responsible for a finite residual compressibility, are present in the density distribution. Finally, we study the robustness of the superfluid phase against thermal fluctuations.
Motivated by recent experiments with ultracold polar molecules trapped in deep optical lattices, we study ground-state properties of the site-diluted long-ranged XXZ model. Site dilution results in off-diagonal disorder. We map the spin model to a hard-core Bose-Hubbard model and perform large-scale Monte Carlo simulations by the Worm algorithm. In absence of site-dilution, we find that, for large enough interaction, three phases are stabilized: a superfluid phase, a checkerboard solid phase, only present at density m = 0.5, and a checkerboard supersolid phase which can be reached by doping the CB phase away from half-filling. In the presence site-dilution and at fixed density m = 0.5, we find that, unlike what observed in the case of short-range hopping, localization never occurs even for site dilution larger than the percolation threshold, and off-diagonal order, though strongly suppressed, persists for arbitrarily large values of site-dilution. arXiv:1804.02426v2 [cond-mat.dis-nn]
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