Functional-derivative study of the Hubbard model. I. Perturbation method and first-order approximation

Tadashi Arai, Morrel H. Cohen, M. P. Tosi

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8 Scopus citations


In order to study the properties of the Hubbard model for narrow bands, a systematic treatment of the equations of motion of the Green's functions appropriate to that model has been developed. Higher-order Green's functions are reduced to functional derivatives of the basic Green's function G and calculated iteratively in a perturbation scheme which takes the Hubbard I solution G0 as the zeroth-order Green's function. A zeroth-order approximation to the self-energy correction obtained by inserting G0 into the functional derivatives is compared with various existing solutions. The perturbation scheme is further extended to an infinite order and the self-energy is calculated exactly up to terms linear in the hopping motion ε, a result which has not been obtained previously. The self-energy correction in this final result is drastically different from the zeroth-order solution, demonstrating the importance of the infinite-order iterative procedure. Finally, the electron correlations included in the final result are discussed in terms of diagrams.

Original languageEnglish (US)
Pages (from-to)1817-1835
Number of pages19
JournalPhysical Review B
Issue number4
StatePublished - 1977
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Condensed Matter Physics


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