Coupled First-Order Transitions In A Fermi-Bose Mixture

Abstract

A model of a mixture of spinless fermions and spin-zero hardcore bosons, with filling fractions ${\rho }_F$ and ${\rho }_B$, 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 ${\rho }_F+{\rho }_B=1$, the fermion hopping amplitude $\varphi$ and boson superfluid amplitude $\psi$ are calculated in the ground state within a mean-field approximation. The Fermi sector is insulating ($\varphi =0$) and the Bose sector is normal ($\psi =0$) for $0\le {\rho }_F<{\rho }_c$. The model has {\em coupled first-order} transitions at ${\rho }_F={\rho }_c\simeq 0.3$ where both $\varphi$ and $\psi$ are discontinuous. The Fermi sector is metallic ($\varphi >0$) 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 Hove singularity, the bulk modulus $\kappa$ displays a cusp-like singularity, the system has a density wave (DW) order, and $\varphi$ 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 of Fermi band dispersions and Fermi surfaces as a function of ${\rho }_F$ 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.

9 pages, 9 figures

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