Analyzing the success of T-matrix diagrammatic theories in representing a modified Hubbard model
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 (Verga et al 2005 Phys. Rev. B 71 155111) 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 (Zlatić et al 2000 Phys. Rev. B 63 035104).
- Publication:
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Journal of Physics Condensed Matter
- Pub Date:
- May 2011
- DOI:
- 10.1088/0953-8984/23/20/205603
- arXiv:
- arXiv:1010.3383
- Bibcode:
- 2011JPCM...23t5603P
- Keywords:
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- Condensed Matter - Strongly Correlated Electrons
- E-Print:
- Includes modified discussion of 1st-order phase transition. Accepted for publication in J. Phys.: Condensed Matter