Competing chiral and multipolar electric phases in the extended Falicov-Kimball model

We study the effects of interband hybridization within the framework of an extended Falicov-Kimball model with itinerant $c$ and $f$ electrons. An explicit interband hybridization breaks the U(1) symmetry associated with the conservation of the difference between the total number of particles in each band. As a result, the degeneracy between multipolar electric and chiral orderings is lifted. We analyze the weak- and strong-coupling limits of the $c$-$f$ electron Coulomb interaction at zero temperature, and derive the corresponding mean-field quantum phase diagrams at half-filling for a model defined on a square lattice.