Extended Falicov-Kimball model: exact solution for the ground state

Abstract

The extended Falicov-Kimball model is analyzed exactly in the ground state at half filling in the limit of large dimensions. In the model the on-site and the intersite density-density interactions between all particles are included. We determined the model's phase diagram and found a discontinuous transition between two different charge-ordered phases. Our analytical calculations show that the ground state of the system is insulating for any nonzero values of the interaction couplings. We also show that the dynamical mean-field theory and the static broken-symmetry Hartree-Fock mean-field approximation give the same results for the model at zero temperature. In addition, we prove using analytical expressions that at infinitesimally small, but finite, temperatures the system can be metallic.

10 pages, 7 figures, 72 references; pdf-ReVTeX class; submitted to Physical Review B

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• Unsupervised Machine Learning Phase Classification for Falicov-Kimball Model
• Extended Falicov-Kimball model at weak onsite and intersite Coulomb interactions
• Charge-Ordered States and the Phase Diagram of the Extended Hubbard Model on the Bethe lattice
• Phase structure of the one-dimensional ${\mathbb{Z}}_2$ lattice gauge theory with second nearest-neighbor interactions