Coexistence Regime and Thermal Crystallization in the cavity-mediated extended Bose-Hubbard Model

Abstract

By means of path integral- Monte Carlo, we study the finite-temperature behavior of the extended Bose-Hubbard model with cavity-mediated long-range interactions at unit filling. At zero temperature, the system supports superfluid, Mott-insulating, supersolid, and charge-density-wave phases, with a strongly first-order transition between superfluid and charge density wave states characterized by a broad coexistence region. Focusing on this coexistence regime, we explore how the dominant order evolves with temperature. When the system is initialized in a superfluid state, the superfluid density is progressively suppressed upon heating, and a normal fluid is stabilized. Upon further increasing the temperature, a thermally assisted emergence of crystalline order occurs which eventually melts into the normal fluid. In contrast, simulations initialized in a charge-density-wave configuration display a smooth thermal melting of density order, with no reemergence of superfluid coherence. Overall, our results show that metastability persists at low temperatures, but ultimately disappears at higher temperatures, where thermally induced crystallization takes place.