Paramagnetic phases of strongly correlated ultracold fermions coupled to an optical cavity

We numerically study a gas of two-component fermions coupled to a transversely pumped optical cavity and confined to a two-dimensional static square optical lattice. In the dispersive regime, the steady state of the system is described by an extended Hubbard Hamiltonian with cavity-mediated long-range interactions. Using real-space dynamical mean-field theory (RDMFT), we investigate the formation of the (superradiant) checkerboard density-wave phase. Our analysis focuses on paramagnetic phases both at quarter and half filling. At quarter filling, we find a reentrant homogeneous Fermi liquid to density wave phase transition with increasing temperature, which is due to the higher entropy of the ordered phase. At half filling, in addition to the Fermi liquid to Mott insulator phase transition, marked by a vanishing quasiparticle residue at the Fermi level, we identify the transition into a density-wave phase. Due to perfect Fermi surface nesting at half filling, we find that arbitrarily small long-range interactions destabilize the system towards the density-wave phase in the absence of short-range interactions. By varying short- and long-range interactions at a fixed low temperature, we obtain the full phase diagram and identify a region of coexistence between the homogeneous Fermi liquid and Mott insulating phase with the density-wave phase. In this region, we determine the thermodynamic phase transition by comparing the energies of the different RDMFT solutions.