[figure: 9.7 cm]

GROUND STATES OF S = 1/2 FALICOV-KIMBALL MODEL

J. Wojtkiewicz^{b} and R. Lemański^{a}

aInstitute of Low Temperatures and Structure Research, Polish Academy of Sciences

P.O.Box 1410, 50-950 Wrocław bDepartment for Mathematical Methods in Physics Warsaw University, Hoża 74, 00-682 Warszawa, Poland

The Falicov-Kimball model with spin 1/2, as proposed by Brandt et al. and used to describe electronic properties of rare-earth compounds, is considered. It describes two sorts of electrons: itinerary d electrons and static f ones. The Hamiltonian consists of the ”classical part” H_{0} and the ”quantum” part V, where

H_{0} = U ∑_{i;σ,η} d_{i,σ}^{†}d_{i,σ}f_{i,η}^{†}f_{i,η} + μ_{d} ∑_{i;σ} d_{i,σ}^{†}d_{i,σ} + μ_{f} ∑_{i;η} f_{i,η}^{†}f_{i,η}

V = −t ∑_{<ij>;σ} (d_{i,σ}^{†}d_{j,σ} + d_{j,σ}^{†}d_{i,σ})

where i, j are site indices; σ, η – spin indices; d_{i,σ}^{†}, d_{i,σ}, f_{i,η}^{†}, f_{i,η} are creation and annihilation operators of the corresponding particles; U – Coulomb repulsion between d and f electrons; t – hopping constant; μ_{d}, μ_{f} – chemical potentials. We assume infinite Coulomb repulsion between f-electrons. The model is considered in the perturbative regime t << U. At the Conference we will present the following results: i) calculation of an effective Hamiltonian up to fourth order in the perturbation theory; ii) analysis of its ground states; there are certain similarities and differences to their counterparts for the spinless FK model). The relationship of our results to experimental data will be also supplied.

[figure: 13.4 cm]

Subject category :

1. Correlated Electrons and High Temperature Superconductors

Presentation mode : oral

Corresponding author : J. Wojtkiewicz

Address for correspondence : Department for Mathematical Methods in Physics Warsaw University, Hoża 74, 00-682 Warszawa, Poland

Email address : wjacek@fuw.edu.pl