Abstract We investigate the thermal melting of the incompressible lobes in the extended Bose-Hubbard Model for bothpure and disordered systems, motivated by recent experimental realizations using ultracold Rydberg atoms inoptical lattices. By tuning the Rydberg excitation level and the lattice spacing, one can engineer the systemto effectively have (i) only the nearest-neighbor interaction or (ii) nearest-neighbor and next-nearest-neighborinteractions. For both these schemes, we employ a mean-field framework to map out the finite-temperature phasediagrams. It is observed that the conventional Mott-insulating and density-wave lobes gradually transform intoa normal fluid with increasing temperature. The melting temperature of the Mott lobes is controlled by theon-site interaction, while that of the density-wave lobes is governed by its nearest-neighbor counterpart. Wealso 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 highertemperatures. Instead, it starts occupying a larger area in the phase diagram. The formalism that we presenthere is capable of treating long-range interactions, disorder, and finite temperature all at once. Moreover, itis versatile enough so that it can be extended to study other forms of disorder, and also be tailored to includelonger-range interactions.
Kabiraj et al. (Fri,) studied this question.