Mean-field phase diagram of the extended Bose-Hubbard model of many-body cavity quantum electrodynamics

We investigate the mean-field phase diagram of the Bose-Hubbard model with infinite-range interactions in two dimensions. This model describes ultracold bosonic atoms confined by a twodimensional optical lattice and dispersively coupled to a cavity mode with the same wavelength as the lattice. We determine the ground-state phase diagram for a grand-canonical ensemble by means of analytical and numerical methods. Our results mostly agree with the ones reported in Dogra et al. [PRA 94, 023632 (2016)], and have a remarkable qualitative agreement with the quantum Monte Carlo phase diagrams of Flottat et al. [PRB 95, 144501 (2017)]. The salient differences concern the stability of the supersolid phases, which we discuss in detail. Finally, we discuss differences and analogies between the ground state properties of strong long-range interacting bosons with the ones predicted for repulsively interacting dipolar bosons in two dimensions.Fil: Himbert, Lukas. Saarland University; Theoretical Physics; Alemania. Universitat Saarland; AlemaniaFil: Cormick, Maria Cecilia. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba. Instituto de Física Enrique Gaviola. Universidad Nacional de Córdoba. Instituto de Física Enrique Gaviola; ArgentinaFil: Kraus, Rebecca. Saarland University; Theoretical Physics; Alemania. Universitat Saarland; AlemaniaFil: Sharma, Shraddha. Saarland University; Theoretical Physics; Alemania. Universitat Saarland; AlemaniaFil: Morigi, Giovanna. Saarland University; Theoretical Physics; Alemania. Universitat Saarland; Alemani