Coupled First-Order Transitions In A Fermi-Bose Mixture

A model of a mixture of spinless fermions and spin-zero hardcore bosons, with filling fractions ρ_F and ρ_B, respectively, on a two-dimensional square lattice with {\em composite} hopping t is presented. In this model, hopping swaps the locations of a fermion and a boson at nearest-neighbor sites. When ρ_F+ρ_B=1, the fermion hopping amplitude φ and boson superfluid amplitude ψ are calculated in the ground state within a mean-field approximation. The Fermi sector is insulating $φ=0$ and the Bose sector is normal $ψ=0$ for 0 le ρ_F < ρ_c. The model has {\em coupled first-order} transitions at ρ_F = ρ_c simeq 0.3 where both φ and ψ are discontinuous. The Fermi sector is metallic (φ>0) and the Bose sector is superfluid (ψ>0) for ρ_c < ρ_F < 1. At ρ_F=1/2, fermion density of states ρ has a van Hove singularity, the bulk modulus κ displays a cusp-like singularity, the system has a density wave (DW) order, and φ and ψ are maximum. At ρ_F=ρ_κ simeq 0.81, κ vanishes, becoming {\em negative} for ρ_κ<ρ_F<1. The role of composite hopping in the evolution of Fermi band dispersions and Fermi surfaces as a function of ρ_F is highlighted. The estimate for BEC critical temperature is in the subkelvin range for ultracold atom systems and several hundred kelvins for possible solid-state examples of the model.