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.

Figures (10)

• Figure 1: Ground-state phase diagram of the Bose--Hubbard model with cavity-mediated long-range interactions [Eq. (\ref{['eq:H']})] at unit filling. The horizontal axis denotes the onsite repulsion $U_s/t$, and the vertical axis shows the ratio of the cavity-mediated long-range interaction to the onsite interaction, $U_\ell/U_s$. Four stable phases are identified: superfluid (SF), Mott insulator (MI), supersolid (SS), and charge-density wave CDW(2,0). Solid lines denote second-order phase boundaries, and solid symbols indicate the numerically determined transition points obtained from QMC simulations. Dashed lines mark first-order transitions, while the shaded region highlights the coexistence windows in which both phases constitute competing free energy minima. Notably, compared to previous studies, the SF–CDW coexistence region is significantly broader, indicating a strongly first-order character of the transition.
• Figure 2: Finite-size scaling analysis of the superfluid–supersolid transition at fixed on-site interaction $U_s/t = 5$. The scaled structure factor $S(\pi,\pi)L^{1.0366}$ is plotted as a function of $U_\ell/U_s$ for system sizes $L=12$ (red squares), 14 (blue triangles), 16 (green triangles), and 24 (gray circles). The intersection of the curves determines the critical point $(U_\ell/U_s)_c = 0.733 \pm 0.005$. Inset: Data callapse using eq. (\ref{['corrected_scaling']}), see text for details.
• Figure 3: Finite-size scaling analysis of the charge density wave--supersolid transition at fixed $U_\ell/U_s = 0.6$. The scaled superfluid density $\rho_s L$ is plotted as a function of $U_s/t$ for system sizes $L=10$ (black circles), 12 (red squares), 14 (blue triangles), and 16 (green triangles). The common intersection of the curves determines the critical point $U_s/t = 10.25 \pm 0.1$. Inset: Data collapse using critical exponents of $(2 + 1)$-dimensional XY universality class.
• Figure 4: (a) Superfluid density $\rho_s$ and (b) structure factor $S(\pi,\pi)$ as functions of $U_\ell/U_s$ at fixed $U_s/t=15$, $L=20$. The data are obtained by increasing (blue symbols) and decreasing (red symbols) the ratio $U_\ell/U_s$, using the final equilibrium configuration of each simulation as the initial state for the next point. The hysteretic behavior demonstrates that the superfluid--charge density wave transition is of first order. From the separation between the forward and backward sweeps, we determine the coexistence region to lie within $0.47\lesssim U_\ell/U_s\lesssim0.73$.
• Figure 5: Temperature evolution of the superfluid density $\rho_s$, compressibility $\kappa$, and structure factor $S(\pi,\pi)$ for $U_s/t = 15$, $U_\ell/U_s = 0.55$, $L=20$, starting from a superfluid initial configuration. As temperature increases, $\rho_s$ decreases and vanishes at $T/t \sim 1.0$, leaving the system in a normal state. At higher temperature, $S(\pi,\pi)$ becomes finite and exhibits a sharp peak around $T/t \approx 3.3$, revealing a thermally stabilized charge density wave ordering before eventually melting into a featureless normal fluid state.