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Journal of Physics C Solid State Physics

A lower bound for the free energy of the Hubbard model

W.‐H. Steeb

Published Apr 7, 1975• 2 citations
Publisher

Abstract

A lower bound for the free energy of the Hubbard model is given. As a point of comparison the authors consider upper bounds. Numerical calculations were performed for the half-filled case and the simple cubic lattice.
DOI
10.1088/0022-3719/8/7/003

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A new variational method is developed to calculate the ground state energy of Fermi systems with strong short-range correlations. A trial wave function of Gutzwiller's type contains additional variational parameters corresponding to configurations of pairs of nearest-neighbor sites. To evaluate the ground state energy, generalized Kikuchi's pseudo-ensemble method is used. The Hubbard model at half band-filling is investigated. The ground state energy of the paramagnetic phase is calculated for a chain, square and simple cubic lattices. It is shown that the short-range order lowers drastically the ground state energy of the Hubbard model at intermediate interaction strength. The paramagnetic phase of the Kondo-Hubbard model (S=1/2S=1/2S=1/2 and S=5/2S=5/2S=5/2) at half band-filling is investigated. The ground state energy, correlation functions and effective mass are calculated for chain, square and simple cubic lattices. A quantum phase transition was found for simple cubic lattice.