Geodesic
A~method of~self-consistent perturbation theory with respect to~the energy overlap integral in~the Hubbard model
Teoretičeskaâ i matematičeskaâ fizika, Tome 85 (1990) no. 3, pp. 412-427

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It is shown that there exists a regular representation for the self-energy part in the form of a series in powers of the energy overlap integral $t(f-f')$. The Green's function that arises in the first order in $t(f-f')$ satisfies four exact relations for the spectral moments corresponding to the linear canonical Kalashnikov–Fradkin transformation and is the best single-particle approximation of the problem on the class of solutions with two delta functions. The self-consistent second order of the theory in $t(f-f')$ gives a basis for the following conclusions: Convergence of the theory is ensured in the regions of concentrations corresponding to a ferromagnetic metal, $n>n_c+\Delta n_f$, and a paramagnetic metal, $n$; in the region $n_c+\Delta n_f>n>n_c-\Delta n_p$ the results of the theory must be interpreted as interpolation results ($n_c$ is the critical concentration of the ferromagnetic–paramagnetic transition, $0\Delta n_f\Delta n_p$). 
@article{TMF_1990_85_3_a6,
     author = {E. G. Goryachev and E. V. Kuz'min},
     title = {A~method of~self-consistent perturbation theory with respect to~the energy overlap integral in~the {Hubbard} model},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {412--427},
     publisher = {mathdoc},
     volume = {85},
     number = {3},
     year = {1990},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1990_85_3_a6/}
}
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E. G. Goryachev; E. V. Kuz'min. A~method of~self-consistent perturbation theory with respect to~the energy overlap integral in~the Hubbard model. Teoretičeskaâ i matematičeskaâ fizika, Tome 85 (1990) no. 3, pp. 412-427. http://geodesic.mathdoc.fr/item/TMF_1990_85_3_a6/