Geodesic
Spectral properties of three-electron systems in the Hubbard model
Teoretičeskaâ i matematičeskaâ fizika, Tome 179 (2014) no. 3, pp. 387-405 Cet article a éte moissonné depuis la source Math-Net.Ru

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We investigate spectral properties of a three-electron system in the Hubbard model framework. We prove that the essential spectrum of the system in a quartet state consists of a single segment and the three-electron bound state is absent. We show that the essential spectrum of the system in doublet states is the union of at most three segments. We also prove that three-electron bound states exist in doublet states.
Keywords: Hubbard model, three-electron system, quartet state, triplet state, doublet state, singlet state, essential spectrum, discrete spectrum, three-electron bound state, discrete Schrödinger operator. 
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S. M. Tashpulatov. Spectral properties of three-electron systems in the Hubbard model. Teoretičeskaâ i matematičeskaâ fizika, Tome 179 (2014) no. 3, pp. 387-405. http://geodesic.mathdoc.fr/item/TMF_2014_179_3_a6/

[1] J. Hubbard, Proc. R. Soc. Lond. A, 276:1365 (1963), 238–257 | DOI

[2] M. C. Gutzwiller, Phys. Rev. Lett., 10:5 (1963), 159–162 | DOI

[3] J. Kanamori, Prog. Theor. Phys., 30:3 (1963), 275–289 | DOI | Zbl

[4] P. W. Anderson, Phys. Rev., 124:1 (1961), 41–53 | DOI | MR

[5] S. P. Shubin, S. V. Wonsowsky, Proc. R. Soc. Lond. A, 145 (1934), 159–180 | DOI

[6] B. V. Karpenko, V. V. Dyakin, G. L. Budrina, FMM, 61:2 (1986), 702–706

[7] D. Mattis, Rev. Modern Phys., 58:2 (1986), 361–379 | DOI | MR

[8] E. Lieb, Phys. Rev. Lett., 62:10 (1989), 1201–1204 | DOI | MR

[9] A. M. Tsvelick, P. B. Wiegmann, Adv. Phys., 32:4 (1983), 453–713 | DOI

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

[11] M. Rid, B. Saimon, Metody sovremennoi matematicheskoi fiziki, v. 1, Funktsionalnyi analiz, Mir, M., 1977 | MR

[12] M. A. Naimark, Normirovannye koltsa, Nauka, M., 1968 | MR

[13] V. V. Valkov, S. G. Ovchinnikov, O. P. Petrakovskii, FTT, 30:10 (1988), 3044–3047

[14] T. Ichinose, Trans. Amer. Math. Soc., 235 (1978), 75–113 | DOI | MR | Zbl

[15] T. Ichinose, Trans. Amer. Math. Soc., 237 (1978), 223–254 | DOI | MR | Zbl

[16] T. Ichinose, “On the spectral properties of tensor products of linear operators in Banach spaces”, Spectral Theory, Banach Center Publications, 8, PWN-Polish Sci. Publ., Warsaw, 1982, 295–300 | MR