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arXiv:cond-mat/9907121 · Physical Review Letters

Competition between Phase Separation and “Classical” Intermediate Valence in an Exactly Solved Model

Woonki Chung, James K. Freericks

Published Mar 13, 2000• 12 citations
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Abstract

The exact solution of the spin-1 / 2 Falicov-Kimball model on an infinite-coordination Bethe lattice is analyzed in the regime of "classical" intermediate valence. We find that (i) either phase separation or a direct metal-insulator transition precludes intermediate valence over a large portion of the phase diagram, and (ii) within the intermediate valence phase, only continuous transitions are found as functions of the localized f-electron energy or temperature.

DOI
10.1103/physrevlett.84.2461

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The exact solution of the spin-1 / 2 Falicov-Kimball model on an infinite-coordination Bethe lattice is analyzed in the regime of "classical" intermediate valence. We find that (i) either phase separation or a direct metal-insulator transition precludes intermediate valence over a large portion of the phase diagram, and (ii) within the intermediate valence phase, only continuous transitions are found as functions of the localized f-electron energy or temperature.
The spin-12\frac{1}{2}21​ Falicov-Kimball model is solved exactly on an infinite-coordination-number Bethe lattice in the thermodynamic limit. This model is a paradigm for a charge-transfer metal-insulator transition, where the occupancy of localized and delocalized electronic orbitals rapidly changes at the metal-insulator transition (rather than the character of the electronic states changing from insulating to metallic as in a Mott-Hubbard transition). The exact solution displays both continuous and discontinuous (first-order) transitions.
The spinless Falicov-Kimball model is solved exactly in the limit of infinite dimensions on both the hypercubic and Bethe lattices. The competition between segregation, which is present for large U,U,U, and charge-density-wave order, which is prevalent at moderate U,U,U, is examined in detail. We find a rich phase diagram that displays both of these phases. The model also shows nonanalytic behavior in the charge-density-wave transition temperature when UUU is large enough to generate a correlation-induced gap in the single-particle density of states.
We examine the one-dimensional spinless Falicov-Kimball model extended by a hybridization potential between the localized and itinerant electron states. Below half-filling we find a crossover from a mixed-valence metal to an integer-valence phase-separated state with increasing on-site Coulomb repulsion. This crossover regime is characterized by local competition between the strong- and weak-coupling behaviour, manifested by the formation of an electronic polaron liquid. A phase diagram is presented and discussed in detail.
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.
The extrapolation of small-cluster exact-diagonalization calculations is used to examine the influence of correlated hopping on valence and metal-insulator transitions in the one-dimensional Falicov-Kimball model. It is shown that in the half-filled band case the ground-state phase diagram as well as the picture of valence and metal-insulator transitions found for the conventional Falicov-Kimball model (without correlated hopping) are strongly changed when the correlated hopping term is added. The effect of correlated hopping is so strong that it can induce the insulator-metal transition. Outside half-filling correlated hopping stabilizes the segregated phase in the ground-state, however, the nature of the ground-state remains qualitatively unchanged.
In this work, we study the extended Falicov-Kimball model at half-filling within the Hartree-Fock approach (HFA) (for various crystal lattices) and compare the results obtained with the rigorous ones derived within the dynamical mean field theory (DMFT). The model describes a system, where electrons with spin-↓ are itinerant (with hopping amplitude t), whereas those with spin-↑ are localized. The particles interact via on-site U and intersite V density-density Coulomb interactions. We show that the HFA description of the ground state properties of the model is equivalent to the exact DMFT solution and provides a qualitatively correct picture also for a range of small temperatures. It does capture the discontinuous transition between ordered phases at U = 2V for small temperatures as well as correct features of the continuous order-disorder transition. However, the HFA predicts that the discontinuous boundary ends at the isolated-critical point (of the liquid-gas type) and it does not merge with the continuous boundary. This approach cannot also describe properly a change of order of the continuous transition for large V as well as various metal-insulator transitions found within the DMFT.