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Equivalence of the Falicov-Kimball and Brandt-Mielsch forms for the free energy of the infinite-dimensional Falicov-Kimball model

A. M. Shvaika·J. K. Freericks
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Abstract

Falicov and Kimball proposed a real-axis form for the free energy of the Falicov-Kimball model that was modified for the coherent potential approximation by Plischke. Brandt and Mielsch proposed an imaginary-axis form for the free energy of the dynamical mean field theory solution of the Falicov-Kimball model. It has long been known that these two formulae are numerically equal to each other; an explicit derivation showing this equivalence is presented here.

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A. M. Shvaika, J. K. Freericks. 2002-11-20. Equivalence of the Falicov-Kimball and Brandt-Mielsch forms for the free energy of the infinite-dimensional Falicov-Kimball model. https://doi.org/10.1103/physrevb.67.153103

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