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

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 $\varphi=45^\circ$, 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 $\theta$. For weak interactions, the system remains superfluid for all $\theta$. Above a critical interaction strength, the superfluid phase becomes unstable and gives way to checkerboard, stripe, or incompressible phases depending on $\theta$. For $\theta\gtrsim 62^\circ$, 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 $\theta$ 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.