Thermal melting of incompressible phases in pure and disordered extended Bose-Hubbard models

We investigate the thermal melting of the incompressible lobes in the extended Bose-Hubbard Model for both pure and disordered systems, motivated by recent experimental realizations using ultracold Rydberg atoms in optical lattices. By tuning the Rydberg excitation level and the lattice spacing, one can engineer the system to effectively have (i) only the nearest-neighbor interaction or (ii) nearest-neighbor and next-nearest-neighbor interactions. For both these schemes, we employ a mean-field framework to map out the finite-temperature phase diagrams. It is observed that the conventional Mott-insulating and density-wave lobes gradually transform into a normal fluid with increasing temperature. The melting temperature of the Mott lobes is controlled by the on-site interaction, while that of the density-wave lobes is governed by its nearest-neighbor counterpart. We also observe that the inclusion of disorder lowers the melting temperatures of both these insulating phases. The additional Bose-glass phase that appears in the presence of disorder, however, does not vanish at higher temperatures. Instead, it starts occupying a larger area in the phase diagram. The formalism that we present here is capable of treating long-range interactions, disorder, and finite temperature all at once. Moreover, it is versatile enough so that it can be extended to study other forms of disorder, and also be tailored to include longer-range interactions.