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 
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/
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     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},
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Voir la notice de l'article provenant de la source Math-Net.Ru

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).

[1] Hubbard J., Proc. Roy. Soc., 276A (1963), 238–257 | DOI

[2] Anderson P. W., Phys. Rev. B, 115 (1959), 2–20 | DOI | MR

[3] Anderson P. W., Mar. Res. Bull., 8 (1973), 153–158 | DOI

[4] Bari R. A., Kaplan T. A., Phys. Rev. Lett., 33A (1970), 400–405 | DOI

[5] Hubbard J., Proc. Roy. Soc., 281A (1964), 401–419 | DOI

[6] Fukuyama H., Ehrenreich H., Phys. Rev., 7 (1973), 3266–3274 | DOI

[7] Nagaoka Y., Phys. Rev., 147 (1966), 392–411 | DOI

[8] Brinkman W. F., Rice T. M., Phys. Rev. B, 2 (1970), 1324–1338 | DOI | MR

[9] Goryachev E. G., Kuzmin E. V., Phys. Lett. A, 131 (1988), 481–489 | DOI

[10] Goryachev E. G., Kuzmin E. V., Phys. Lett. A, 137 (1989), 423–426 | DOI

[11] Izyumov Yu. A., Skryabin Yu. N., Statisticheskaya mekhanika magnitouporyadochennykh sistem, Nauka, M., 1987 | MR

[12] Tyablikov S. V., Metody kvantovoi teorii magnetizma, Nauka, M., 1975 | MR

[13] Plakida N. M., Phys. Lett. A, 43 (1973), 481–489 | DOI | MR

[14] Kalashnikov O. K., Fradkin E. S., ZhETF, 55 (1968), 607–619

[15] Goryachev E. G., Kuzmin E. V., Ovchinnikov S. G., J. Phys. C, 15 (1982), 1481–1493 | DOI

[16] Goryachev E. G., Kuzmin E. V., ZhETF, 91 (1986), 902–911

[17] Goryachev E. G., Kuzmin E. V., Fazovaya diagramma ferromagnitnogo metalla s nevyrozhdennoi zonoi v rezhime silnoi khabbardovskoi korrelyatsii, 1, Preprint No 574F, SO AN SSSR, Krasnoyarsk, 1989