Abstract
We consider the three-electron systems in the impurity Hubbard model and investigated the spectra of the system in the second doublet state in the ν-dimensional lattice Zν.
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References
P. W. Anderson, “Localized magnetic states in metals,” Phys. Rev., 124, 41–53 (1961).
M. C. Gutzwiller, “Effect of correlation on the ferromagnetism of transition metals,” Phys. Rev. Lett., 10, 159–162 (1963).
J. Hubbard, “Electron correlations in narrow energy bands,” Proc. R. Soc. London Ser. A Math. Phys. Eng. Sci., 276, 238–257 (1963).
T. Ichinose, “Spectral properties of tensor products of linear operators, 1,” Trans. Am. Math. Soc., 235, 75–113 (1978).
T. Ichinose, “Spectral properties of tensor products of linear operators, 2: The approximate point spectrum and Kato essential spectrum,” Trans. Am. Math. Soc., 237, 223–254 (1978).
T. Ichinose, “Tensor products of linear operators. Spectral theory,” Banach Center Publ., 8, 294–300 (1982).
U. A.Izyumov and Yu. N. Skryabin, Statistical Mechanics of Magnetically Ordered Systems [in Russian], Nauka, Moscow (1987).
J. Kanamori, “Electron correlation and ferromagnetism of transition metals,” Prog. Theoret. Phys., 30, 275–289 (1963).
B. V. Karpenko, V. V.Dyakin, and G. L. Budrina, “Two electrons in the Hubbard Model,” Phys. Metal. Phys. Metallurgy, 61, No. 4, 702–706 (1986).
E. Lieb, “Two theorems on the Hubbard model,” Phys. Rev. Lett., 62, 1201–1204 (1989).
D. Mattis, “The few-body problems on a lattice,” Rev. Modern Phys., 58, 370–379 (1986).
M. Reed and B. Simon, Methods of Modern Mathematical Physics, Acad. Press, New York (1978).
S. P. Shubin and S. V. Wonsowsky, “On the electron theory of metals,” Proc. R. Soc. London Ser. A Math. Phys. Eng. Sci., 145, 159–180 (1934).
S. M.Tashpulatov, “Spectral properties of three-electron systems in the Hubbard model,” Theor. Math. Phys., 179, No. 3, 387–405 (2014).
A. M. Tsvelick and P. B. Wiegman,“Exact results in the theory of magnetic alloys,” Adv. Phys., 32, 453–713 (1983).
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Translated from Sovremennaya Matematika. Fundamental’nye Napravleniya (Contemporary Mathematics. Fundamental Directions), Vol. 65, No. 1, Contemporary Problems in Mathematics and Physics, 2019.
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Tashpulatov, S.M. Spectra of the Energy Operator of Three-Electron Systems in the Impurity Hubbard Model. Second Doublet State. J Math Sci 265, 103–116 (2022). https://doi.org/10.1007/s10958-022-06048-8
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DOI: https://doi.org/10.1007/s10958-022-06048-8