Physics – Mathematical Physics
Scientific paper
2001-07-05
Commun. Math. Phys. 227, 243-279 (2002)
Physics
Mathematical Physics
34 pages
Scientific paper
10.1007/s002200200632
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.
Freericks James K.
Lieb Elliott H.
Ueltschi Daniel
No associations
LandOfFree
Segregation in the Falicov-Kimball model does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Segregation in the Falicov-Kimball model, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Segregation in the Falicov-Kimball model will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-652625