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arXiv · 1010.3383

Analyzing the success of T-matrix diagrammatic theories in representing a modified Hubbard model

P. Pisarski·R. J. Gooding
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Abstract

We present a systematic study of various forms of renormalization that can be applied in the calculation of the self-energy of the Hubbard model within the T-matrix approximation. We compare the exact solutions of the attractive and repulsive Hubbard models, for linear chains of lengths up to eight sites, with all possible taxonomies of the T-matrix approximation. For the attractive Hubbard model, the success of a minimally self-consistent theory found earlier in the atomic limit (Phys. Rev. B 71, 155111 (2005)) is not maintained for finite clusters unless one is in the very strong correlation limit. For the repulsive model, in the weak correlation limit at low electronic densities -- that is, where one would expect a self-consistent T-matrix theory to be adequate -- we find the fully renormalized theory to be most successful. In our studies we employ a modified Hubbard interaction that eliminates all Hartree diagrams, an idea which was proposed earlier (Phys. Rev. B 63, 035104 (2000)).

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P. Pisarski, R. J. Gooding. 2011-04-04. Analyzing the success of T-matrix diagrammatic theories in representing a modified Hubbard model. https://doi.org/10.1088/0953-8984%2F23%2F20%2F205603

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