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A model of a mixture of spinless fermions and spin-zero hardcore bosons, withfilling fractions $\rho_F$ and $\rho_B$, respectively, on a two-dimensionalsquare 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 $\rho_F+\rho_B=1$, the fermion hopping amplitude $\phi$ and bosonsuperfluid amplitude $\psi$ are calculated in the ground state within amean-field approximation. The Fermi sector is insulating ($\phi=0$) and theBose sector is normal ($\psi=0$) for $0 \le \rho_F < \rho_c$. The model has{\em coupled first-order} transitions at $\rho_F = \rho_c \simeq 0.3$ whereboth $\phi$ and $\psi$ are discontinuous. The Fermi sector is metallic($\phi>0$) and the Bose sector is superfluid ($\psi>0$) for $\rho_c < \rho_F <1$. At $\rho_F=1/2$, fermion density of states $\rho$ has a van Hovesingularity, the bulk modulus $\kappa$ displays a cusp-like singularity, thesystem has a density wave (DW) order, and $\phi$ and $\psi$ are maximum. At$\rho_F=\rho_{\kappa} \simeq 0.81$, $\kappa$ vanishes, becoming {\em negative}for $\rho_{\kappa}<\rho_F<1$. The role of composite hopping in the evolution ofFermi band dispersions and Fermi surfaces as a function of $\rho_F$ ishighlighted. The estimate for BEC critical temperature is in the subkelvinrange for ultracold atom systems and several hundred kelvins for possiblesolid-state examples of the model.

Coupled First-Order Transitions In A Fermi-Bose Mixture