Fluid structure of 1D spinful Fermi gases with long-range interactions

We discuss the fluid structure in the quantum phases of a 1D spinful Fermi gas of atoms interacting via an infinitely long-range coupling, as it may result from a photon-mediated two-body coupling in optical cavities. The system reveals a rich physics, where the spin/charge-density wave and superfluid-like order compete with each other. Following our previous work based on a combined mean-field, exact diagonalization and bosonization analysis, we provide the phase diagram of the system and discuss the structure of the fluid, addressing the main features in momentum space of the order parameters, momentum distribution and two-body correlations. We highlight that the nesting of the Fermi surface in 1D ultimately drives the formation of periodic structures commensurate with the cavity-induced mean-field potential.