Geodesic
Exact spin states and analytic formulas for nonequilibrium spin transport in a three-site one-dimensional system with interacting electrons
Teoretičeskaâ i matematičeskaâ fizika, Tome 209 (2021) no. 3, pp. 515-542 Cet article a éte moissonné depuis la source Math-Net.Ru

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We choose a typical three-site one-dimensional (1D) quantum chain system to deduce exact spin states and nonequilibrium spin transport properties analytically. The initial spin-up and spin-down electron charges on each site of the chain are calculated from the exactly derived spin ground state with the assumption of half-filling. Based on the Keldysh formalism, we describe the basic theoretical methods and derive some analytic formulas (differential spin conductance, spin transport current, electron charge distribution, etc.) for nonequilibrium spin transport of the 1D chain systems within the Hartree–Fock approximation when Coulomb electron interaction is present. The scattering processes including Coulomb repulsion between the spin-up and spin-down electrons, and spin–spin interactions due to spin degrees freedom are taken into account. We also report the numerical results of the nonequilibrium spin transport of the three-site 1D chain system in some special cases using the initial spin-up/down electron charges.
Keywords: one-dimensional quantum chain system, spin states, nonequilibrium spin transport, Keldysh formalism, Hartree–Fock approximation. 
@article{TMF_2021_209_3_a7,
     author = {Yangdong Zheng},
     title = {Exact spin states and analytic formulas for nonequilibrium spin transport in a three-site one-dimensional system with interacting electrons},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {515--542},
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}
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Yangdong Zheng. Exact spin states and analytic formulas for nonequilibrium spin transport in a three-site one-dimensional system with interacting electrons. Teoretičeskaâ i matematičeskaâ fizika, Tome 209 (2021) no. 3, pp. 515-542. http://geodesic.mathdoc.fr/item/TMF_2021_209_3_a7/

[1] I. Žutić, J. Fabian, S. Das Sarma, “Spintronics: Fundamentals and applications”, Rev. Modern Phys., 76:2 (2004), 323–410, arXiv: cond-mat/0405528 | DOI

[2] V. Baltz, A. Manchon, M. Tsoi, T. Moriyama, T. Ono, Y. Tserkovnyak, “Antiferromagnetic spintronics”, Rev. Modern Phys., 90:1 (2018), 015005, 57 pp. | DOI

[3] S. Nonoyama, A. Oguri, Y. Asano, S. Maekawa, “Numerical study of the effect of Coulomb repulsion on resonant tunneling”, Phys. Rev. B, 50:4 (1994), 2667–2670 ; “Study of the effect of Coulomb repulsion on resonant tunneling in magnetic fields”, J. Phys. Soc. Japan, 64:10 (1995), 3871–3880 | DOI | DOI

[4] C. W. J. Beenakker, “Excess conductance of a spin-filtering quantum dot”, Phys. Rev. B, 73:20 (2006), 201304, 4 pp., arXiv: cond-mat/0601638 | DOI

[5] G. Giavaras, J. H. Jefferson, M. Fearn, C. J. Lambert, “Singlet-triplet filtering and entanglement in a quantum dot structure”, Phys. Rev. B, 75:8 (2007), 085302, 6 pp., arXiv: cond-mat/0611207 | DOI

[6] J. Schwinger, “Brownian motion of a quantum oscillator”, J. Math. Phys., 2:3 (1961), 407–432 | DOI

[7] L. V. Keldysh, “Diagrammnaya tekhnika dlya neravnovesnykh protsessov”, ZhETF, 47:4 (1964), 1515–1527

[8] C. Caroli, R. Combescot, P. Nozieres, D. Saint-James, “A direct calculation of the tunnelling current. II. Free electron description”, J. Phys. C, 4:16 (1971), 2598–2610 | DOI

[9] S. Hershfield, J. H. Davies, J. W. Wilkins, “Resonant tunneling through an Anderson impurity. I. Current in the symmetric model”, Phys. Rev. B, 46:11 (1992), 7046–7060 | DOI

[10] Y. Meir, N. S. Wingreen, P. A. Lee, “Transport through a strongly interacting electron system: Theory of periodic conductance oscillations”, Phys. Rev. Lett., 66:23 (1991), 3048–3051 | DOI

[11] S. Datta, Electronic Transport in Mesoscopic Systems, Cambridge Univ. Press, Cambridge, 1995

[12] S. Ajisaka, F. Barra, “Nonequilibrium mesoscopic Fermi-reservoir distribution and particle current through a coherent quantum system”, Phys. Rev. B, 87:19 (2013), 195114, 6 pp., arXiv: 1302.0232 | DOI

[13] E. M. Lifshits, L. P. Pitaevskii, Teoreticheskaya fizika, v. 9, Statisticheskaya fizika. Chast 2. Teoriya kondensirovannogo sostoyaniya, Fizmatlit, M., 2004 ; т. 10, Физическая кинетика, 2002 | MR | MR

[14] Y. Meir, N. S. Wingreen, “Landauer formula for the current through an interacting electron region”, Phys. Rev. Lett., 68:16 (1992), 2512–2515 | DOI

[15] D. Goldhaber-Gordon, H. Shtrikman, D. Mahalu, D. Ambusch-Magder, U. Meirav, M. A. Kastner, “Kondo effect in a single-electron transistor”, Nature, 391:6663 (1998), 156–159 | DOI

[16] Y. Zheng, H. Mizuta, S. Oda, “Theoretical study of nonequilibrium electron transport and charge distribution in a three-site quantum wire”, Japan J. Appl. Phys., 47:1R (2008), 371–382 | DOI

[17] Y. Zheng, H. Mizuta, S. Oda, “Nonequilibrium transport properties for a three-site quantum wire model”, Phys. Stat. Sol. C, 5:1, 56–60 | DOI