Slave boson theory of the extended Falicov-Kimball model

TL;DR

This paper applies the slave boson theory to the extended Falicov-Kimball model, revealing how orbital structure, hybridization, and correlations influence phase transitions, including insulating and excitonic states.

Contribution

It provides a detailed analysis of the phase diagram of the extended Falicov-Kimball model using slave boson theory, highlighting deviations from Hartree-Fock predictions.

Findings

Correlated-insulating state at strong interactions for degenerate orbitals

Discontinuous valence transitions with finite orbital energy difference

Excitonic insulator phase only in degenerate orbitals with zero hybridization

Abstract

The extended Falicov-Kimball model, with both an on-site hybridization potential and dispersive narrow band, is examined within the saddle-point approximation to the Kotliar-Ruckenstein slave boson theory. We first set the hybridization potential to zero and find that the phase diagram depends strongly upon the orbital structure: for degenerate orbitals, a correlated-insulating state is found at sufficiently strong interaction strengths, whereas a finite orbital energy difference can lead to discontinuous valence transitions. The obtained phase diagram is very sensitive to the presence of a finite hybridization potential. As in Hartree-Fock theory, we find an enhancement of the hybridization by the inter-orbital Coulomb repulsion. The more precise treatment of correlation effects, however, leads to large deviations from the Hartree-Fock results. In the limit of vanishing hybridization an excitonic insulator state is only found when the orbitals are degenerate, which restricts this phase to a much smaller parameter space than in other available mean-field theories.