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arXiv:cond-mat/9412092 · Nuclear Physics B

Functional integrals for Hubbard operators and projection methods for strong interaction

Eberhard O. Tüngler, Thilo Kopp

Published Jun 1, 1995• 8 citations
arXivHTMLPDF
DOI
10.1016/0550-3213(95)00148-l

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Abstract The effect of the static approximation in the functional integral representation of the paramagnetic Hubbard model is critically investigated. The exactly solvable two‐site model is treated within the one‐ and two‐field static functional integral method and some thermodynamic properties (local magnetic moment, specific heat cv) are compared with the exact solution for various interaction strengths and electron densities. It is shown that the static functional integral theory yields unphysical results for cv in the strong interacting system at small densities. The two‐field and one‐field methods are preferable in the low‐ and high‐temperature regions, respectively.
We study the quasiparticle spectrum of the Hubbard model by using a projection-operator formalism of the Green's function. In the weak-electron-correlation regime, we obtain the exact results up to second order in the intra-atomic interaction. For strong electron correlations, the quasiparticle spectrum consists of two bands. For each band, the quasiparticle energy is obtained exactly up to the first order in the transfer integral. We also propose a semiclassical approximation which gives the above-mentioned exact results in proper limits.