Abstract
The Falicov–Kimball model consists of spinless electrons and classical particles (ions) on a lattice. The electrons hop between nearest neighbor sites, while the ions do not. We consider the model with equal numbers of ions and electrons and with a large on-site attractive force between ions and electrons. For densities 1/4 and 1/5, the ion configuration in the ground state had been proved to be periodic. We prove that for density 2/9 it is periodic as well. However, for densities between 1/4 and 1/5 other than 2/9 we prove that the ion configuration in the ground state is not periodic. Instead there is phase separation. For densities in (1/5, 2/9) the ground-state ion configuration is a mixture of the density 1/5 and 2/9 ground-state ion configurations. For the interval (2/9, 1/4) it is a mixture of the density 2/9 and 1/4 ground states.
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REFERENCES
U. Brandt and R. Schmidt, Ground state properties of a spinless Falicov-Kimball model, Z. Phys. B 67:43 (1986).
J. K. Freericks and L. M. Falicov, Two-state one-dimensional spinless Fermi gas, Phys. Rev. B 41:2163 (1990).
C. Gruber, J. Jedrzejewski, and P. Lemberger, Ground states of the spinless Falicov-Kimball model. II, J. Stat. Phys. 66:913 (1992).
C. Gruber and N. Macris, The Falicov-Kimball model: a review of exact results and extensions, Helv. Phys. Acta 69:851 (1996).
T. Kennedy, Some rigorous results on the ground states of the Falicov-Kimball model, Rev. Math. Phys. 6:901–925 (1994). Also in The State of Matter, Michael Aizenman and Hizihiro Araki, eds. (World Scientific, 1994).
T. Kennedy and E. H. Lieb, An itinerant electron model with crystalline or magnetic long range order, Physica 138A:320–358 (1986).
P. Lemberger, Segregation in the Falicov-Kimball Model, J. Phys. A: Math. Gen. 25:715 (1992).
G. I. Watson, Repulsive particles on a two-dimensional lattice, Physica 246A:253–274 (1997).
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Kennedy, T. Phase Separation in the Neutral Falicov–Kimball Model. Journal of Statistical Physics 91, 829–843 (1998). https://doi.org/10.1023/A:1023023230602
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DOI: https://doi.org/10.1023/A:1023023230602