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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.