Lower bound for the segregation energy in the Falicov-Kimball model

Details Lower bound for the segregation energy in the Falicov-Kimball model Lower bound for the segregation energy in the Falicov-Kimball model

2002-11-10

arxiv.org/abs/cond-mat/0211183v1

Physics

Condensed Matter

Strongly Correlated Electrons

8 pages, 2 figures

Scientific paper

10.1088/0305-4470/36/9/302

In this work, a lower bound for the ground state energy of the Falicov-Kimball model for intermediate densities is derived. The explicit derivation is important in the proof of the conjecture of segregation of the two kinds of fermions in the Falicov-Kimball model, for sufficiently large interactions. This bound is given by a bulk term, plus a term proportional to the boundary of the region devoid of classical particles. A detailed proof is presented for density n=1/2, where the coefficient 10^(-13) is obtained for the boundary term, in two dimensions. With suitable modifications the method can also be used to obtain a coefficient for all densities.

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