Thermocrystallization of lattice dipolar bosons coupled to a high-finesse cavity

Investigating finite-temperature effects on quantum phases is key to their experimental realization. Finite temperature and the interplay between quantum and thermal fluctuations can undermine properties and/or key features of quantum systems, but they can also bring about interesting phenomena. In this paper we present a comprehensive investigation of the finite-temperature phase diagram of two-dimensional lattice dipolar bosons coupled to a high-finesse optical cavity. Interestingly, we observe that checkerboard density-density correlations are enhanced at finite temperature. Indeed, we found that finite temperature drives a superfluid ground state into a normal state, which will then develop checkerboard order at higher temperatures. We show that this effect is solely due to the cavity-mediated interactions. We also confirm that the supersolid checkerboard phase survives for a wide range of filling factors up to a temperature scale of the order of half hopping amplitude, while the checkerboard diagonal order can survive up to temperatures of a few hopping amplitudes.