Canonical phase diagrams of the 1D Falicov-Kimball model at T = 0

Abstract

The Falicov-Kimball model of spinless quantum electrons hopping on a 1-dimensional lattice and of immobile classical ions occupying some lattice sites, with only intrasite coupling between those particles, have been studied at zero temperature by means of well-controlled numerical procedures. For selected values of the unique coupling parameter U the restricted phase diagrams (based on all the periodic configurations of localized particles (ions) with period not greater than 16 lattice constants, typically) have been constructed in the grand-canonical ensemble. Then these diagrams have been translated into the canonical ensemble. Compared to the diagrams obtained in other studies our ones contain more details, in particular they give better insight into the way the mixtures of periodic phases are formed. Our study has revealed several families of new characteristic phases like the generalized most homogeneous and the generalized crenel phases, a first example of a structural phase transition and a tendency to build up an additional symmetry -the holeparticle symmetry with respect to the ions (electrons) only, as U decreases.

Bosonization Solution of the Falicov-Kimball Model

“…(7) that the Coulomb interaction will shift the f -level downwards, emptying the c-band. The depletion of the c-electron population causes segregation to occur at a smaller value of G than in the CP; the new boundary can be calculated self-consistently from the available numerical results [3]. Using the same curve-fitting technique as for the CP, we find excellent agreement with the data We extend our analysis to the physically interesting limit V ≪t of the QFKM.…”

“…A c-electron spread over more than a single lattice site carries the same charge over these sites: due to the Coulomb interaction G, this will favour empty underlying f -orbitals. Although such "segregation" is known to occur in the CP [3,5], the derivation of the responsible effective interaction is a new achievement in the history of the model.…”

“…The CP assumes fixed c-and f -electron populations, examining the diagonal LRO (or "crystalline order") adopted by the f -electrons in the ground state. In spite of detailed numerical maps of the one-dimensional (1D) FKM's phase diagram [3], its behaviour is only rigorously understood at weak- [4] and strong-coupling [5].…”

Influence of the inter-ion interaction on the phase diagrams of the 1D Falicov–Kimball system

“…This is a lattice model of itinerant electrons and localized ions that are coupled via an on-site interaction. The moving electrons induce an indirect interaction between the ions, bringing about their spatial arrangement [2].At half-filling the ground state is known to be the chessboard phase (where the ions occupy one of two sublattices), whereas the segregated phase (where the ions and electrons reside in separate domains) has a minimum energy far from half-filling. These results were proved for the hypercubic lattice in any dimension [3].…”

“…This is a lattice model of itinerant electrons and localized ions that are coupled via an on-site interaction. The moving electrons induce an indirect interaction between the ions, bringing about their spatial arrangement [2].…”