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arXiv:2608.07608

Density instabilities and thermal stabilization of phase separated states in dipolar lattice bosons

Yaghmorassene Hebib, Stefano Peaquin, Chao Zhang, Vittorio Penna, Barbara Capogrosso-Sansone

Published Aug 6, 2026• 0 citations
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Abstract

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 $φ=45^\circ$, 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 $θ\gtrsim 62^\circ$, 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.

DOI
10.48550/arxiv.2608.07608

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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∘φ=45^\circφ=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 θθθ. For weak interactions, the system remains superfluid for all θθθ. Above a critical interaction strength, the superfluid phase becomes unstable and gives way to checkerboard, stripe, or incompressible phases depending on θθθ. For θ≳62∘θ\gtrsim 62^\circθ≳62∘, we find that half filling becomes unstable and only the empty state, n=0n=0n=0, and the fully filled state, n=1n=1n=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=0n=0n=0 and n=1n=1n=1. At finite temperature, thermal fluctuations shift the onset of density instabilities to larger θθθ 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.
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.
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The two-dimensional square lattice hard-core boson Hubbard model with near-neighbor interactions has a ``checkerboard'' charge density wave insulating phase at half filling and sufficiently large intersite repulsion. When doped, rather than forming a supersolid phase in which long-range charge density wave correlations coexist with a condensation of superfluid defects, the system instead phase separates. However, it is known that there are other lattice geometries and interaction patterns for which such coexistence takes place. In this paper we explore the possibility that anisotropic hopping or anisotropic near-neighbor repulsion might similarly stabilize the square lattice supersolid. By considering the charge density wave structure factor and superfluid density for different ratios of interaction strength and hybridization in the $\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{x}$ and $\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{y}$ directions, we conclude that phase separation still occurs.
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.
Motivated by recent experiments with ultracold magnetic atoms trapped in optical lattices where the orientation of atomic dipoles can be fully controlled by external fields, we study the ground state properties of dipolar bosons trapped in a two-dimensional lattice with density-induced hopping and where the dipoles are tilted along the xzxzxz plane. We present ground state phase diagrams of the above system at different tilt angles. We find that, as the dipolar interaction increases, the superfluid phase at half filling factor is destroyed in favor of either a checkerboard or stripe solid phase for tilt angle θ≲35.3∘\theta \lesssim 35.3^{\circ}θ≲35.3∘ or θ≳35.3∘\theta \gtrsim 35.3^{\circ}θ≳35.3∘ respectively. More interesting physics happens at tilt angles θ≳58∘\theta \gtrsim 58^{\circ}θ≳58∘ where we find that, as the dipolar interaction strength increases, solid phases first appear at filling factor lower than 0.50.50.5. Moreover, unlike what observed at lower tilt angles at half filling, we find that the superfluid gives way to a stripe solid through a stripe supersolid phase.
We consider a minimal model to describe the quantum phases of ultracold dipolar bosons in two-dimensional square optical lattices. The model is a variation of the extended Bose-Hubbard model and apt to study the quantum phases arising from the variation in the tilt angle $\ensuremath{\theta}$ of the dipolar bosons. At low tilt angles, ${0}^{\ensuremath{\circ}}\ensuremath{\leqslant}\ensuremath{\theta}\ensuremath{\lesssim}{25}^{\ensuremath{\circ}}$, the ground states of the system are phases with checkerboard order, which can be either checkerboard supersolids or checkerboard density waves. For high tilt angles, ${35}^{\ensuremath{\circ}}\ensuremath{\lesssim}\ensuremath{\theta}\ensuremath{\lesssim}{55}^{\ensuremath{\circ}}$, phases with striped order of the supersolid or density wave are preferred. In the intermediate domain, ${25}^{\ensuremath{\circ}}\ensuremath{\lesssim}\ensuremath{\theta}\ensuremath{\lesssim}{35}^{\ensuremath{\circ}}$, an emulsion or superfluid phase intervenes the transition between the checkerboard and the striped phases. The attractive interaction dominates at $\ensuremath{\theta}\ensuremath{\gtrsim}{55}^{\ensuremath{\circ}}$, which renders the system unstable, and there is a density collapse. For our studies we use Gutzwiller mean-field theory to obtain the quantum phases and the phase boundaries. In addition, we calculate the phase boundaries between an incompressible and a compressible phase of the system by considering second-order perturbation analysis of the mean-field theory. The analytical results, where applicable, are in excellent agreement with the numerical results. In our study, the incompressible phases have an average occupancy per site $\ensuremath{\rho}\ensuremath{\le}1$, but the compressible phases can have $\ensuremath{\rho}>1$.