Proof of phase separation in the binary-alloy problem: the one-dimensional spinless Falicov-Kimball model

Abstract

The ground states of the one-dimensional Falicov-Kimball model are investigated in the small-coupling limit, using nearly degenerate perturbation theory. For rational electron and ion densities, respectively equal to $\frac{p}{q}$, $\frac{p_i}{q}$, with $p$ relatively prime to $q$ and $\frac{p_i}{q}$ close enough to $\frac{1}{2}$, we find that in the ground state the ion configuration has period $q$. The situation is analogous to the Peierls instability where the usual arguments predict a period-$q$ state that produces a gap at the Fermi level and is insulating. However for $\frac{p_i}{q}$ far enough from $\frac{1}{2}$, this phase becomes unstable against phase separation. The ground state is a mixture of a period-$q$ ionic configuration and an empty (or full) configuration, where both configurations have the same electron density to leading order. Combining these new results with those previously obtained for strong coupling, it follows that a phase transition occurs in the ground state, as a function of the coupling, for ion densities far enough from $\frac{1}{2}$.

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References in corpus (2)

• The Stability of the Peierls Instability for Ring-Shaped Molecules
• Molecule Formation and the Farey Tree in the One-Dimensional Falicov-Kimball Model

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• Charge Order in the Falicov-Kimball Model
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• 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
• Ground-state correlations of itinerant electrons in the spinless Falicov-Kimball chain and related tight-binding systems
• Peierls instability for the Holstein model
• Robust finite-temperature disordered Mott insulating phases in inhomogeneous Fermi-Fermi mixtures with density and mass imbalance
• Thermodynamics of weakly coupled Falicov-Kimball chains from renormalization-group theory