Diagram technique for the Hubbard model. Ladder diagram summation

• Main Authors: Moskalenko, V.A., Kon, L.Z.
• Format: Article
• Language: English
• Published: Інститут фізики конденсованих систем НАН України 1998
• Series: Condensed Matter Physics
• Online Access: http://dspace.nbuv.gov.ua/handle/123456789/118628

A new diagram technique based on the generalized Wick theorem has been elaborated for the systems with strong electronic correlations. Coulomb repulsion of the electrons of the Hubbard model is considered as the main part of Hamiltonian and is taken into account in a zero order approximation. The hopping matrix elements are considered as a perturbation. One-particle Matsubara-Green function of the model has been investigated and Dyson equation has been obtained. New elements of the theory which are characteristic of this new approach are the local many-particle irreducible Green functions, or Kubo cumulants. They become zero when Coulomb interaction is zero. The main task of this paper is the summing of ladder diagrams which take into account the most essential charge and spin fluctuations of the system. The integral equations, which sum such diagrams, have been established for two different channels. The coherent potential approximation has been used to simplify and solve these equations. On this basis a metal-dielectric phase transition has been investigated.