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 interactions, 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 a fixed half-integer filling factor for which the clean system is either a superfluid at a lower dipolar interaction strength or a checkerboard solid at a larger dipolar interaction strength. We find that, even for weak dipolar interactions, superfluidity is destroyed in favor of a Bose glass at a relatively low disorder strength. Interestingly, in the presence of disorder, superfluidity persists for values of the dipolar interaction strength for which the clean system is a checkerboard solid. At a 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.
Recent advances in realizing nearly degenerate dipolar gases in optical lattices have enabled the study of quantum systems with long-range anisotropic interactions. Here, we investigate hard-core dipolar bosons on a two-dimensional square lattice described by an extended Bose--Hubbard model. Using path-integral quantum Monte Carlo simulations at fixed azimuthal angle
φ=45∘, we investigate density instabilities arising from first-order phase transitions. We start by mapping the ground-state phase diagram at half filling as a function of dipolar interaction strength and polar angle
θ. For weak interactions, the system remains superfluid for all
θ. Above a critical interaction strength, the superfluid phase becomes unstable and gives way to checkerboard, stripe, or incompressible phases depending on
θ. For
θ≳62∘, we find that half filling becomes unstable and only the empty state,
n=0, and the fully filled state,
n=1, are stable. Unlike recent experimental reports of a self-bound insulator at half filling, the homogeneous ground state does not support such a phase, but instead exhibits a direct first-order transition between
n=0 and
n=1. At finite temperature, thermal fluctuations shift the onset of density instabilities to larger
θ and stabilize intermediate fillings in the regime where half filling is unstable in the ground state. This leads to phase-separated states consisting of empty and fully filled regions that resemble the experimentally observed "self-bound insulator." In a harmonic trap, similar structures also emerge from phase coexistence associated with the underlying first-order transition.
Disorder is ubiquitous in condensed matter systems, but a thorough understanding of these systems is hindered by poor control over the nature of disorder and competing interactions. Ultracold gases trapped in optical lattices, on the other hand, offer an unprecedented level of control over interactions and disorder, and are ideal candidates to test theoretical predictions and study fascinating phenomena resulting from the interplay between disorder, interaction, and quantum degeneracy. In this dissertation, I present my research on strongly correlated many-body lattice bosons in the presence of disordered potentials. My results are based on quantum Monte Carlo simulations by the Worm algorithm. Experimentally, lattice bosons can be realized by ultracold gases in optical lattices. I studied the ground state phase diagram of the above systems in the presence of diagonal (quasi-periodic disordered potential or random disordered potential) and off-diagonal disorder (in the form of site dilution). First, I will discuss the ground state phase diagram of two-dimensional bosons in quasi-periodic lattices. Then, I will discuss the phase diagram as well as finite temperature thermodynamic properties of two-dimensional dipolar lattice bosons in the presence of random diagonal disordered potentials. Finally, I will discuss the phase diagram of two-dimensional hard-core lattice bosons system in the presence of long-range hopping and long-range two-body interactions both in the absence of disorder and in the presence of site dilution (equivalent to off-diagonal disorder). This system is equivalent to the long-range XXZ model as realized by polar molecules trapped in a deep optical lattice. These results provide theoretical guidance for experimentalists to find quantum phase transitions as well as exotic quantum phases in strongly correlated bosonic lattice systems.
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 find no evidence of a Mott-glass-like behavior.
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.
The recent advances in creating nearly degenerate quantum dipolar gases in optical lattices are opening the doors for the exploration of equilibrium physics of quantum systems with anisotropic and long-range dipolar interactions. In this paper we study the zero- and finite-temperature phase diagrams of a system of hard-core dipolar bosons at half-filling, trapped in a two-dimensional square optical lattice. The dipoles are aligned parallel to one another and tilted out of the optical lattice plane by means of an external electric field. At zero-temperature, the system is a superfluid (SF) at all tilt angles θ provided that the strength of dipolar interaction is below a critical value . Upon increasing the interaction strength while keeping θ fixed, the SF phase is destabilized in favor of a checkerboard or a stripe solid (SS) depending on the tilt angle. We explore the nature of the phase transition between the two solid phases, identifying a region of metastable emulsion states intervening between the two solid lobes. Additionally, we study the stability of these quantum phases against thermal fluctuations and find that the SS is the most robust, making it the best candidate for experimental observation.
We study the phase diagram of a system of soft-core dipolar bosons confined to a two-dimensional optical lattice layer. We assume that dipoles are aligned perpendicular to the layer such that the dipolar interactions are purely repulsive and isotropic. We consider the full dipolar interaction and perform Path Integral Quantum Monte Carlo simulations using the Worm Algorithm. Besides a superfluid phase, we find various solid and supersolid phases. We show that, unlike what was found previously for the case of nearest-neighboring interaction, supersolid phases are stabilized not only by doping the solids with particles but with holes as well. We further study the stability of these quantum phases against thermal fluctuations. Finally, we discuss pair formation and the stability of the pair checkerboard phase formed in a bilayer geometry, and suggest experimental conditions under which the pair checkerboard phase can be observed.