Segregation in the Falicov-Kimball model

Abstract

The Falicov-Kimball model is a simple quantum lattice model that describes light and heavy electrons interacting with an on-site repulsion; alternatively, it is a model of itinerant electrons and fixed nuclei. It can be seen as a simplification of the Hubbard model; by neglecting the kinetic (hopping) energy of the spin up particles, one gets the Falicov-Kimball model. We show that away from half-filling, i.e. if the sum of the densities of both kinds of particles differs from 1, the particles segregate at zero temperature and for large enough repulsion. In the language of the Hubbard model, this means creating two regions with a positive and a negative magnetization. Our key mathematical results are lower and upper bounds for the sum of the lowest eigenvalues of the discrete Laplace operator in an arbitrary domain, with Dirichlet boundary conditions. The lower bound consists of a bulk term, independent of the shape of the domain, and of a term proportional to the boundary. Therefore, one lowers the kinetic energy of the itinerant particles by choosing a domain with a small boundary. For the Falicov-Kimball model, this corresponds to having a single `compact' domain that has no heavy particles.

34 pages

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• Pattern formation in mixtures of ultracold atoms in optical lattices
• Segregation in the asymmetric Hubbard model
• Minimizing the ground state energy of an electron in a randomly deformed lattice
• Formation of charge and spin ordering in strongly correlated electron systems
• Dynamical mean-field theory for light fermion--heavy boson mixtures on optical lattices
• Ground state phase diagram of a spinless, extended Falicov-Kimball model on the triangular lattice
• Sharp spectral estimates in domains of infinite volume
• Ferromagnetism of the Hubbard Model at Strong Coupling in the Hartree-Fock Approximation
• Thermodynamic studies of the two dimensional Falicov-Kimball model on a triangular lattice
• Formation of charge-stripe phases in a system of spinless fermions or hardcore bosons
• Charge Order in the Falicov-Kimball Model
• Momentum distribution and ordering in mixtures of ultracold light and heavy fermionic atoms
• Gapless regime in the charge density wave phase of the finite dimensional Falicov-Kimball model
• Lower bound for the segregation energy in the Falicov-Kimball model
• Electronic transport through correlated electron systems with nonhomogeneous charge orderings
• On the nature of striped phases: Striped phases as a stage of "melting" of 2D crystals
• Phase separation in the combined Falicov-Kimball and static Holstein model
• Unsupervised Machine Learning Phase Classification for Falicov-Kimball Model
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• Infinite temperature spin dynamics in the asymmetric Hatsugai-Kohmoto model
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• Anomalous Quantum Relaxation in the Infinite Temperature Hubbard Chain