Exact analytic solution of the infinite-dimensional extended Falicov-Kimball model: the phase diagram and thermodynamic properties

The Falicov-Kimball model [1] is a simplified version of the Hubbard model, where only electrons with, e.g., spin down, are itinerant and the other are localized. We discuss results for the extended Falicov-Kimball model at half-filling on the Bethe lattice in the large-dimension limit derived within the dynamical mean field theory formalism [2-3]. On-site U and intersite V density-density interactions between particles occupying neighboring sites are included in the Hamiltonian [2-5]. We determined the exact phase diagrams of the model both in the ground state [2] and at finite temperatures [3]. Using analytical formulas and having calculated the temperature dependent density of states we studied thermodynamic properties of the system starting from its free energy. We compared the results with those obtained within the standard Hartree-Fock approach [4,5].
References:
[1] L.M. Falicov, J.C. Kimball, Phys. Rev. Lett. 22, 997 (1969)
[2] R. Lemanski, et al., Phys. Rev. B 96, 205102 (2017)
[3] K.J. Kapcia, et al., Phys. Rev. B 99, 245143 (2019)
[4] K.J. Kapcia, et al., J. Phys: Condens. Matter (2020), in press
[5] K.J. Kapcia, et al., Condens. Matter Phys. (2020), in press