Geodesic
Structure of the essential spectrum and discrete spectrum of the energy operator of four-electron systems in the impurity Hubbard model. The third triplet state
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the Voronezh international winter mathematical school "Modern methods of function theory and related problems", Voronezh, January 27 - February 1, 2023, Part 3, Tome 229 (2023), pp. 53-82.

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The structure of the essential spectrum and the discrete spectrum of the energy operator of four-electron systems in the Hubbard impurity model for the third triplet state of the system are examined. The following statements are proved. (a) The essential spectrum of the third triplet is the union of three segments and the discrete spectrum of the third triplet is empty. (b) The essential spectrum of the third triplet is the union of eight segments and the discrete spectrum of the third triplet consists of three eigenvalues. (c) The essential spectrum of the third triplet is the union of sixteen segments and the discrete spectrum of the third triplet consists of eleven eigenvalues.
Keywords: Hubbard model, Hubbard impurity model, four-electron system, triplet state, essential spectrum, discrete spectrum 
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S. M. Tashpulatov; R. T. Parmanova. Structure of the essential spectrum and discrete spectrum of the energy operator of four-electron systems in the impurity Hubbard model. The third triplet state. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the Voronezh international winter mathematical school "Modern methods of function theory and related problems", Voronezh, January 27 - February 1, 2023, Part 3, Tome 229 (2023), pp. 53-82. http://geodesic.mathdoc.fr/item/INTO_2023_229_a6/

[1] Tashpulatov S. M., “O spektralnykh svoistvakh trekhelektronnykh sistem v modeli Khabbarda”, Teor. mat. fiz., 179:3 (2014), 387–405 | DOI | Zbl

[2] Anderson P. W., “Localized magnetic states in metals”, Phys. Rev., 124 (1961), 41–53 | DOI | MR

[3] Gutzwiller M. C., “Effect of correlation on the ferromagnetism of transition metals”, Phys. Rev. Lett., 10 (1963), 159–162 | DOI

[4] Hubbard J., “Electron correlations in narrow energy bands”, Proc. Roy. Soc. A., 276 (1963), 238–257 | MR

[5] Ichinose T., “Spectral properties of tensor products of linear operators, 1”, Trans. Am. Math. Soc., 235 (1978), 75–113 | DOI | MR | Zbl

[6] Ichinose T., “Spectral properties of tensor products of linear operators, 2. The approximate point spectrum and Kato essential spectrum”, Trans. Am. Math. Soc., 237 (1978), 223–254 | MR | Zbl

[7] Ichinose T., “On the spectral properties of tensor products of linear operators in Banach spaces”, Spectral Theory, v. 8, PWN-Polish Scientific Publishers, Warsaw, 1982, 294–300 | MR

[8] Izyumov Yu. A., Skryabin Yu. N., Statistical Mechanics of Magnetically Ordered Systems, Nauka, Moscow, 1988 (in Russian) | MR

[9] Kanamori J., “Electron correlation and ferromagnetism of transition metals”, Prog. Theor. Phys., 30 (1963), 275–289 | DOI | Zbl

[10] Karpenko B. V., Dyakin V. V., Budrina G. L., “Two electrons in the Hubbard Model”, Phys. Met. Metallogr., 61 (1986), 702–706

[11] Lieb E., “Two theorems on the Hubbard Model”, Phys. Rev. Lett., 62 (1989), 1201–1204 | DOI | MR

[12] Mattis D., “The few-body problems on a lattice”, Rev. Mod. Phys., 58 (1986), 370–379 | DOI | MR

[13] Reed M., Simon B., Methods of Modern Mathematical Physics. Vol. 1. Functional Analysis, Acad. Press, New York, 1972 | MR

[14] Reed M., Simon B., Methods of Modern Mathematical Physics. Vol. 4. Operator Analysis, Academic Press, New York, 1982 | MR

[15] Shubin S. P., Wonsowsky S. V., “On the electron theory of metals”, Proc. Roy. Soc. A., 145 (1934), 159–172

[16] Tashpulatov S. M., “Spectral Properties of three-electron systems in the Hubbard Model”, J. Phys. Conf. Ser., 697:012025 (2016), 1–25 | MR

[17] Tashpulatov S. M., “The structure of essential spectra and discrete spectrum of four-electron systems in the Hubbard model in a singlet state”, Lobachevskii J. Math., 38:3 (2017), 530–541 | DOI | MR | Zbl

[18] Tsvelick A. M., Wiegman P. B., “Exact results in the theory of magnetic alloys”, Adv. Phys., 32:4 (1983), 453–713 | DOI | MR

[19] Valkov V. V., Ovchinnikov S. G., Petrakovskii O. P., “The Excitation Spectra of two-magnon systems in easy-axis quasidimensional Ferromagnets”, Sov. Phys. Solid State., 30 (1986), 3044–3047