Charge Order in the Falicov-Kimball Model

Abstract

We examine the spinless one-dimensional Falicov-Kimball model (FKM) below half-filling, addressing both the binary alloy and valence transition interpretations of the model. Using a non-perturbative technique, we derive an effective Hamiltonian for the occupation of the localized orbitals, providing a comprehensive description of charge order in the FKM. In particular, we uncover the contradictory ordering roles of the forward-scattering and backscattering itinerant electrons: the latter are responsible for the crystalline phases, while the former produces the phase separation. We find an Ising model describes the transition between the phase separated state and the crystalline phases; for weak-coupling we present the critical line equation, finding excellent agreement with numerical results. We consider several extensions of the FKM that preserve the classical nature of the localized states. We also investigate a parallel between the FKM and the Kondo lattice model, suggesting a close relationship based upon the similar orthogonality catastrophe physics of the associated single-impurity models.

arXiv comment39 pages, 6 figures

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Cited by in corpus (5)

• Numerical study of magnetization processes in rare-earth tetraborides
• Ground-state phase diagrams of the generalized Falicov-Kimball model with Hund coupling
• Electronic transport through correlated electron systems with nonhomogeneous charge orderings
• Realization of a "Two Relaxation Rates" in the Hubbard-Falicov-Kimball Model
• Phase Separation and Charge-Ordered Phases of the d = 3 Falicov-Kimball Model at T>0: Temperature-Density-Chemical Potential Global Phase Diagram from Renormalization-Group Theory