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Systems of Strongly Correlated Electrons Interacting with Each Other and with Phonons: Diagrammatic Approach

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Abstract

The features of materials leading to the strong correlation effect and the phenomena realized in them are considered: the metal-insulator Mott transition and high-temperature superconductivity. The history of their study is traced. Particular attention is paid to studying the role of the interorbital correlation effect and the Hund’s coupling in multiorbital systems as well as the electron-phonon interaction in systems with strong Coulomb interaction. The development of the strong coupling diagram technique is analyzed and the results obtained based on the approach used are presented.

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REFERENCES

  1. Koller, W., Meyer, D., Ono, Y., and Hewson, A.C., First- and second-order phase transitions in the Holstein–Hubbard model, Europhys. Lett., 2004, vol. 66, no. 4, p. 559. https://doi.org/10.1209/epl/i2003-10228-6

    Article  Google Scholar 

  2. Schubin, S.P. and Wonsowskii, S.V., On the electron theory of metals, Proc. R. Soc., 1934, vol. A145, no. 854, p. 159.

  3. Schubin, S. and Vonsowsky, S., Zur Elektronentheorie der Metalle I, Phys. Zs. UdSSR, 1935, vol. 7, no. 1, p. 292.

    Google Scholar 

  4. Schubin, S. and Vonsowsky, S., Zur Elektronentheorie der Metalle II, Phys. Zs. UdSSR, 1936, vol. 10, no. 3, p. 348.

    Google Scholar 

  5. Bogolyubov, P.I. and Tyablikov, P.V., On one application of perturbation theory to the polar model of a metal, Zh. Eksp. Teor. Fiz., 1949, vol. 19, no. 3, p. 251.

    Google Scholar 

  6. Bogolyubov, P.I. and Tyablikov, P.V., An approximate method for finding the lowest energy levels of electrons in a metal, Zh. Eksp. Teor. Fiz., 1949, vol. 19, p. 256.

    Google Scholar 

  7. Hubbard, J., Electron correlations in narrow energy bands, Proc. R. Soc. A, 1963, vol. 276, no. 1365, p. 238. https://doi.org/10.1098/rspa.1963.0204

    Article  Google Scholar 

  8. Hubbard, J., Electron correlations in narrow energy bands II. The degenerate band case, Proc. R. Soc. A, 1694, vol. 277, no. 1369, p. 237. https://doi.org/10.1098/rspa.1964.0019

    Article  Google Scholar 

  9. Hubbard, J., Electron correlations in narrow energy bands III. An improved solution, Proc. R. Soc. A, 1964, vol. 281, no. 1386, p. 401. https://doi.org/10.1098/rspa.1964.0190

    Article  Google Scholar 

  10. Hubbard, J., Electron correlations in narrow energy bands IV. The atomic representation, Proc. R. Soc. A, 1965, vol. 285, no. 1403, p. 542. https://doi.org/10.1098/rspa.1965.0124

    Article  MathSciNet  Google Scholar 

  11. Hubbard, J., Electron correlations in narrow energy bands V. A perturbation expansion about the atomic limit, Proc. R. Soc. A, 1967, vol. 296, no. 1444, p. 82. https://doi.org/10.1098/rspa.1967.0007

    Article  Google Scholar 

  12. Hubbard, J., Electron correlations in narrow energy bands VI. The connection with many-body perturbation theory, Proc. R. Soc. A, 1967, vol. 296, no. 1444, p. 100. https://doi.org/10.1098/rspa.1967.0008

    Article  Google Scholar 

  13. Anderson, P.W., Localized magnetic states in metals, Phys. Rev., 1961, vol. 124, no. 1, p. 4. https://doi.org/10.1103/PhysRev.124.41

    Article  MathSciNet  Google Scholar 

  14. Richard, P., Sato, T., Nakayama, K., Souma, S., et al., Angle-resolved photoemission spectroscopy of the Fe-based Ba0.6K0.4Fe2As2 high temperature superconductor: Evidence for an orbital selective electron-mode coupling, Phys. Rev. Lett., 2009, vol. 102, p. 047003. https://doi.org/10.1103/PhysRevLett.102.047003

    Article  Google Scholar 

  15. Oshnama, A., Saito, S., Hamada N., and Iyamoto, Y., Electronic structures of C60 fullerides and related materials, J. Phys. Chem. Solids, 1992, vol. 53, no. 11, p. 1457. doi 90239-Ahttps://doi.org/10.1016/0022-3697(92)

  16. Georges, A., de’Medici, L., and Mravlje, J., Strong correlations from Hund’s coupling, Annu. Rev. Cond. Matter Phys., 2013, vol. 4, no. 1, p. 137. https://doi.org/10.1146/annurev-conmatphys-020911-125045

    Article  Google Scholar 

  17. Gweon, Gh., Sasagawa, T., Zhou, S., et al., An unusual isotope effect in a high-transition-temperature superconductor, Nature, 2004, vol. 430, p. 187. https://doi.org/10.1038/nature02731

    Article  Google Scholar 

  18. Franck, J.P., Physical Properties of High Temperature Superconductors IV, Ginsberg, D.M., Ed., Singapore: World Scientific, 1994, p. 189.

    Google Scholar 

  19. Wen-min, H. and Hsiu-hau, L., Anomalous isotope effect in iron-based superconductors, Nat. Sci. Rep., 2019, vol. 9, no. 1, p. 5547. https://doi.org/10.1038/s41598-019-42041-z

    Article  Google Scholar 

  20. Liu, R.H., Wu, T., Wu, G., Chen, H., et al., A large iron isotope effect in SmFeAsO1 − xFx and Ba1 − xKxFe2As2, Nature, 2009, vol. 459, p. 64. https://doi.org/10.1038/nature07981

    Article  Google Scholar 

  21. Shirage, P.M., Kihou, K., Miyaqzawa, K., Lee, Ch.-H., et al., Inverse iron isotope effect on the transition temperature of the (Ba, K)Fe2As2 superconductor, Phys. Rev. Lett., 2009, vol. 103, no. 25, p. 257003. https://doi.org/10.1103/PhysRevLett.103.257003

    Article  Google Scholar 

  22. Khasanov, R., Bendele, M., Bussmann-Holder, A., and Keller, H., Intrinsic and structural isotope effects in iron-based superconductors, Phys. Rev. B, 2010, vol. 82, no. 21, p. 21250. https://doi.org/10.1103/PhysRevB.82.212505

    Article  Google Scholar 

  23. Alexandrov, A.S. and Krebs, A.B., Polarons in high-temperature superconductors, Sov. Phys. Usp., 1992, vol. 35, no. 5, p. 345.

    Article  Google Scholar 

  24. Alexandrov, A.S., Superconducting polarons and bipolarons, in Polarons in Advanced Materials, Alexandrov, A.S., Eds., Springer Series in Materials Science, Dordrecht: Springer, 2007, vol. 103. https://doi.org/10.1007/978-1-4020-6348-0

  25. Moskalenko, V.A., Entel, P., Marinaro, M., and Digor, D.F., Strong interaction of correlated electrons with phonons: Exchange of phonon clouds by polarons, JETP, 2003, vol. 97, no. 3, p. 632.

    Article  Google Scholar 

  26. Holstein, T., Studies of polaron motion: Part I. The molecular-crystal model, Ann. Phys., 1969, vol. 8, no. 3, p. 325. https://doi.org/10.1016/0003-4916(59)90002-8

    Article  Google Scholar 

  27. Theoretical Methods for Strongly Correlated Electrons, CRM Series in Mathematical Physics, Sénéchal, D., Tremblay, A.-M., and Bourbonnais, C., Eds., New York: Springer-Verlag, 2004.

  28. Moskalenko, V.A., Generalized Wick’s theorem for electronic systems with strong correlations, in Voprosy kvantovoi teorii kondensirovannykh sred (Questions of Quantum Theory of Condensed Matter), Khadzhi, P.I., et al., Kishinev: Shtiintsa, 1990.

  29. Vladimir, M.I. and Moskalenko, V.A., Diagram technique for the Hubbard model, Theor. Math. Phys., 1990, vol. 82, no. 3, p. 301. https://doi.org/10.1007/BF01029224

    Article  Google Scholar 

  30. Vonsovskii, P.V., Izyumov, Yu.A., and Kurmayev, E.Z., Sverkhprovodimost’ perekhodnykh metallov, ikh splavov i soedinenii (Superconductivity of Transition Metals, Their Alloys and Compounds), Moscow: Nauka, 1977.

  31. De Boer, J.H. and Verwey, E.J.W., Semi-conductors with partially and with completely filled 3d-lattice bands, Proc. Phys. Soc., 1937, vol. 49, no. 59, p. 59. https://doi.org/10.1088/0959-5309/49/4S/307

    Article  Google Scholar 

  32. Mott, N.F., The basis of the electron theory of metals, with special reference to the transition metals, Proc. Phys. Soc. A, 1949, vol. 62, p. 416. https://doi.org/10.1088/0370-1298/62/7/303

    Article  Google Scholar 

  33. Mott, N.F. and Peierls, R., Discussion of the paper by de Boer and Verwey, Proc. Phys. Soc., 1937, vol. 49, no. 4S, p. 72. https://doi.org/10.1088/0959-5309/49/4S/308

    Article  Google Scholar 

  34. Mott, N.F., On the transition to metallic conduction in semiconductors, Canad. J. Phys., 1956, vol. 34, no. 12A, p. 1356. https://doi.org/10.1139/p56-151

    Article  Google Scholar 

  35. Mott, N.F., The transition to the metallic state, Philos. Mag., 1961, vol. 6, no. 62, p. 287. https://doi.org/10.1080/14786436108243318

    Article  Google Scholar 

  36. Mott, N.F., Metal–Insulator Transitions, Taylor and Francis, 1974.

    Google Scholar 

  37. Imada, M., Fujimori, A., and Tokura, Y., Metal–insulator transitions, Rev. Mod. Phys., 1998, vol. 70, no. 4, p. 1039. https://doi.org/10.1103/PhysRevLett.43.1892

    Article  Google Scholar 

  38. Steglich, F., Aarts, J., Bredl, C.D., Lieke, W.J., et al., Superconductivity in the presence of strong Pauli paramagnetism: CeCu2Si2, Phys. Rev. Lett., 1979, vol. 43, no. 25, p. 1892. https://doi.org/10.1103/PhysRevLett.43.1892

    Article  Google Scholar 

  39. Stewart, G.R., Heavy-fermion systems, Rev. Mod. Phys., 1984, vol. 56, no. 4, p. 755. https://doi.org/10.1103/RevModPhys.56.755

    Article  Google Scholar 

  40. Bednorz, J.G. and Müller, K.A., Possible high Tc superconductivity in the Ba–La–Cu–O system, Z. Phys. B, 1986, vol. 64, no. 2, p. 189. https://doi.org/10.1007/BF01303701

    Article  Google Scholar 

  41. Wu, M.K., Asburn, J.R., Torng, C.J., Hor, P.H., et al., Superconductivity at 93 K in a new mixed-phase Y‒Ba–Cu–O compound system at ambient pressure, Phys. Rev. Lett., 1987, vol. 58, no. 9, p. 908. https://doi.org/10.1103/PhysRevLett.58.908

    Article  Google Scholar 

  42. Putilin, S.N., Antipov, E.V., Chmaissem, O., and Marezio, M., Superconductivity at 94 K in HgBa2CuO4+δ, Nature, 1993, vol. 362, p. 226.

    Article  Google Scholar 

  43. Abakumov, A.M., Antipov, E.V., Kovba, L.M., Kopnin, E.M., et al., Complex oxides with coherent intergrowth structures, Russ. Chem. Rev., 1995, vol. 64, no. 8, p. 769.

    Article  Google Scholar 

  44. Somayazulu, M., Ahart, M., Mishra, A.K., Geballe, Z.M., et al., Evidence for superconductivity above 260 K in lanthanum superhydride at megabar pressures, Phys. Rev. Lett., 2019, vol. 122, no. 2, p. 027001. https://doi.org/10.1103/PhysRevLett.122.027001

    Article  Google Scholar 

  45. Tanigaki, K., Ebbesen, T., Saito, S., Mizuki, J., et al., Superconductivity at 33 K in CsxRbyC60, Nature, 1991, vol. 352, p. 222. https://doi.org/10.1038/352222a0

    Article  Google Scholar 

  46. Palstra, T.T.M., Zhou, O., Iwasa, Y., Sulewski, P.E., et al., Superconductivity at 40K in cesium doped C60, Solid State Commun., 1995, vol. 93, no. 4, p. 327. https://doi.org/10.1016/0038-1098(94)00787-X

    Article  Google Scholar 

  47. Reich, S., Leitus, G., Tssaba, Y., Levi, Y., et al., Localized high-Tc superconductivity on the surface of Na-doped WO3, J. Supercond., 2000, vol. 13, p. 855. https://doi.org/10.1023/A:100786771051

    Article  Google Scholar 

  48. Takahashi, T., Sato, T., Souma, S., Muranaka, T., et al., High-resolution photoemission study of MgB2Tc, Phys. Rev. Lett., 2001, vol. 86, no. 21, p. 4915. https://doi.org/10.1103/PhysRevLett.86.4915

    Article  Google Scholar 

  49. Kamihara, Y., Takumi, W., Hirano, M., and Hosono, H., Iron-based layered superconductor La[O1 – xFx]FeAs (x = 0.05−0.12) with T c = 26 K, Am. Chem. Soc., 2008. vol. 130, no. 11, p. 3296. https://doi.org/10.1021/ja800073m

    Article  Google Scholar 

  50. Meier, W.R., Ding, Q., Kreyssig, A., Bud’ko, S.L., et al., Hedgehog spin-vortex crystal stabilized in a hole-doped iron-based superconductor, npj Quantum Mater., 2018, vol. 3, no. 5. https://doi.org/10.1038/s41535-017-0076-x

  51. Bardeen, J., Cooper, L.N., and Schrieffer, L.R., Microscopic theory of superconductivity, Phys. Rev., 1957, vol. 106, no. 1, p. 162. https://doi.org/10.1103/PhysRev.106.162

    Article  MathSciNet  Google Scholar 

  52. Bardeen, J., Cooper, L.N., and Schrieffer, L.R., Theory of superconductivity, Phys. Rev., 1957, 108, no. 5, p. 1175. https://doi.org/10.1103/PhysRev.108.1175

    Article  MathSciNet  Google Scholar 

  53. Bogoliubov, N.N., A new method in the theory of superconductivity. I, Sov. Phys. JETP, 1958, vol. 34, p. 41.

    MathSciNet  Google Scholar 

  54. Gor’kov, L.P, On the energy spectrum of superconductors, Sov. Phys. JETP, 1958, vol. 7, no. 3, p. 505.

    Google Scholar 

  55. Bogolyubov, N.N., Tolmachev, V.V., and Shirkov, D.V., Novyy metod v teorii sverkhprovodimosti (New Method in the Theory of Superconductivity), Moscow: Izd. Akad. Nauk SSSR, 1958.

  56. Moskalenko, V.A., Superconductivity of metals taking into account the overlap of energy bands, Fiz. Metal. Metalloved., 1959, vol. 8, no. 4, p. 503.

    Google Scholar 

  57. Suhl, H., Matthias, B.T., and Walker, L.R., Bardeen–Cooper–Schrieffer theory of superconductivity in the case of overlapping bands, Phys. Rev. Lett., 1959, vol. 3, p. 552. https://doi.org/10.1103/PhysRevLett.3.552

    Article  Google Scholar 

  58. Palistrant, M.E. and Ursu, V.A., Thermodynamic and magnetic properties of superconductors with anisotropic energy spectrum, MgB2, J. Supercond. Nov. Magn., 2008, vol. 21, no. 3, p. 171. https://doi.org/10.1007/s10948-008-0312-5

    Article  Google Scholar 

  59. Skornyakov, S.L., Efremov, A.V, Skorikov, N.A., Korotin, M.A., et al., Classification of the electronic correlation strength in the iron pnictides: The case of the parent compound BaFe2As2, Phys. Rev. B, 2009, vol. 80, no. 9, p. 092501. https://doi.org/10.1103/PhysRevB.80.092501

    Article  Google Scholar 

  60. Scalapino, D.J., Superconductivity and spin fluctuations, J. Low Temp. Phys., 1999, vol. 117, no. p. 179. https://doi.org/10.1023/A:1022559920049

  61. Hirsch, J.E., Attractive interaction and pairing in fermion systems with strong on-site repulsion, Phys. Rev. Lett., 1985, vol. 54, no. 12, p. 1317. https://doi.org/10.1103/PhysRevLett.54.1317

    Article  Google Scholar 

  62. Scalapino, D.J., Oh, E.L., and Hirsch, J.E., D-wave pairing near a spin-density-wave instability, Phys. Rev. B, 1986, vol. 34, no. 11, p. 8190. https://doi.org/10.1103/physrevb.34.8190

    Article  Google Scholar 

  63. Anderson, P.W., The resonating valence bond state in La2CuO4 and superconductivity, Science, 1987, vol. 235, no. 4793, p. 1196. https://doi.org/10.1126/science.235.4793.1196

    Article  Google Scholar 

  64. Bastide, C., Repulsion-induced superconductivity in a multiband Hubbard model, Phys. Rev. B, 1990, vol. 41, p. 807. Phys. Rev. B, 1991, vol. 43, p. 1210.https://doi.org/10.1103/PhysRevB.41.807

  65. Bastide, C. and Lacroix, C., The Anderson lattice in the weak-hopping limit: Superconductivity induced by dynamic interactions, J. Phys. C: Solid State Phys., 1988, vol. 21, p. 3557. https://doi.org/10.1088/0022-3719/21/19/009

    Article  Google Scholar 

  66. Digor, D.F., Entel, P., Marinaro, M., Moskalenko, V.A., et al., The possibility of forming coupled pairs in the periodic Anderson model, Theor. Math. Phys., 2001, vol. 127, no. 2, p. 664. https://doi.org/10.1023/A:1010401720592

    Article  Google Scholar 

  67. Qin, M., Chung, Ch.-M., Shui, H., Vitali, E., et al., Absence of superconductivity in the pure two-dimensional Hubbard model, Phys. Rev. X, 2020, vol. 10, no. 3, p. 031016. https://doi.org/10.1103/PhysRevX.10.031016

    Article  Google Scholar 

  68. Dong, X., Del Re, L., Toschi, A., and Gull., E., Mechanism of superconductivity in the Hubbard model at intermediate interaction strength, Proc. Natl. Acad. Sci. USA, 2022, vol. 19, no. 33, p. 1. https://doi.org/10.1073/pnas.2205048119

    Article  Google Scholar 

  69. Vollhardt, D., Byczuk, K., and Kollar, M., Dynamical mean-field theory, in Strongly Correlated Systems, Avella, A. and Mancini, F., Eds., Springer Series in Solid-State Sciences, Heidelberg: Springer, 2012, vol. 171, p. 203. https://doi.org/10.1007/978-3-642-21831-6_7

  70. Kotliar, G., Savrasov, S.Y., Haule, K., Oudovenko, V.S., et al., Electronic structure calculations with dynamical mean-field theory, Rev. Mod. Phys., 2006, vol. 78, no. 3, p. 865. https://doi.org/10.1103/RevModPhys.78.865

    Article  Google Scholar 

  71. Georges, A., Kotliar, G, Krauth, W., and Rozenberg, M.J., Dynamical mean-field theory of strongly correlated fermion systems and the limit of infinite dimensions, Rev. Mod. Phys., 1996, 8, vol. 8, no. 13, p. 13. https://doi.org/10.1103/RevModPhys.68.13

  72. Kotliar, G. and Vollhardt, D., Strongly correlated materials: Insights from dynamical mean-field theory, Phys. Today, 2004, vol. 57, no. 3, p. 53. https://doi.org/10.1063/1.1712502

    Article  Google Scholar 

  73. Kubo, R., Generalized cumulant expansion method, J. Phys. Soc. Jpn., 1962, vol. 17, no. 7, p. 1100. https://doi.org/10.1143/JPSJ.17.1100

    Article  MathSciNet  Google Scholar 

  74. Vaks, V.G., Larkin, A.I., and Pikin, S.A., Thermodynamics of an ideal ferromagnetic substance, Sov. Phys. JETP, 1968, vol. 26, no. 1, p. 188.

    Google Scholar 

  75. Izyumov, Yu.A. and Kassan-ogly, F.L., Polevyye metody v teorii ferromagnetizma (Field Methods in the Theory of Ferromagnetism), Moscow: Nauka, 1974.

  76. Slobodyan, P.M. and Stasyuk, I.V., Diagram technique for Hubbard operators, Theor. Math. Phys., 1974, vol. 19, no. 3, p. 616. https://doi.org/10.1007/BF01035575

    Article  Google Scholar 

  77. Zaitsev, R.O., Generalized diagram technique and spin waves in an anisotropic ferromagnet, Sov. Phys. JETP, 1976, vol. 41, no. 3, p. 100.

    Google Scholar 

  78. Izyumov, Yu.A., Katsnel’son, M.I., Skryabin, Yu.N., Magnetizm kollektivizirovannykh elektronov (Magnetism of Itinerant Electrons), Moscow: Fizmatlit, 1994.

  79. Barabanov, A.F., Kikoin, K.A., and Maksimov, L.A., Graphical technique for the generalized Hubbard model, Theor. Math. Phys., 1975, vol. 25, no. 1, p. 997. https://doi.org/10.1007/BF01037645

    Article  Google Scholar 

  80. Barabanov, A.F., Kikoin, K.A., and Maksimov, L.A., Diagram technique for the Anderson model, Theor. Math. Phys., 1974, vol. 20, no. 3., p. 881. https://doi.org/10.1007/BF01040169

    Article  Google Scholar 

  81. Metzner, W., Linked-cluster expansion around the atomic limit of the Hubbard model, Phys. Rev. B, 1991, vol. 43, no. 10, p. 8549. https://doi.org/10.1103/PhysRevB.43.8549

    Article  Google Scholar 

  82. Pairault, S., Sénéchal, D., and Tremblay, A.-M.S., Strong-coupling expansion for the Hubbard model, Phys. Rev. Lett., 1998, vol. 80, no. 24, p. 5389.https://doi.org/10.1103/PhysRevLett.80.5389

  83. Pairault, S., Sénéchal, D., and Tremblay, A.-M.S., Strong-coupling perturbation theory of the Hubbard model, Eur. Phys. J. B, 2000, vol. 16, p. 85. https://doi.org/10.1007/s100510070253

    Article  Google Scholar 

  84. Boies, D., Bourbonnais, C., and Tremblay, A.-M. S., One-particle and two-particle instability of coupled Luttinger liquids, Phys. Rev. Lett., 1995, vol. 74, p. 968. https://doi.org/10.1103/PhysRevLett.74.96

    Article  Google Scholar 

  85. Sarker, S.K., A new functional integral formalism for strongly correlated Fermi systems, J. Phys. C, 1988, vol. 21, no. 18, p. L667. https://doi.org/10.1103/PhysRevLett.57.1362

    Article  Google Scholar 

  86. Sherman, A., One-loop approximation for the Hubbard model, Phys. Rev. B, 2006, vol. 73, no. 15, p. 155105. https://doi.org/10.1103/PhysRevB.73.155105

    Article  Google Scholar 

  87. Barnes, S.E., New method for the Anderson model, J. Phys., 1976, vol. 6, no. 7, p. 1375. https://doi.org/10.1088/0305-4608/6/7/018

    Article  MathSciNet  Google Scholar 

  88. Barnes, S.E., New method for the Anderson model. II. The U = 0 limit, J. Phys., 1977, vol. 7, no. 12, p. 2631. https://doi.org/10.1088/0305-4608/7/12/022

    Article  MathSciNet  Google Scholar 

  89. Coleman, P., New approach to the mixed-valence problem, Phys. Rev. B, 1984, vol. 29, no. 6, p. 3035. https://doi.org/10.1103/PhysRevB.29.3035

    Article  Google Scholar 

  90. Vakaru, S.I., Vladimir, M.I., and Moskalenko, V.A., Diagram technique for the Hubbard model. II. Metal–insulator transition, Theor. Math. Phys., 1990, vol. 85, no. 2, p. 1185. https://doi.org/10.1007/BF01086848

    Article  Google Scholar 

  91. Bogolyubov, N.N. and Moskalenko, V.A., On the existence of superconductivity in the Hubbard model, Theor. Math. Phys., 1991, vol. 86, no. 1, p. 10. https://doi.org/10.1007/BF01018492

    Article  MathSciNet  Google Scholar 

  92. Bogolyubov, N.N. and Moskalenko, V.A., Superconductivity in the Hubbard model with deviation from half filling, Theor. Math. Phys., 1992, vol. 92, no. 2, p. 820. https://doi.org/10.1007/BF01015550

    Article  Google Scholar 

  93. Moskalenko, V.A. and Kon, L.Z., Diagram technique for the Hubbard model. Ladder diagram summation, Cond. Matter Phys., 1998, vol. 1, no. 1, p. 23.

    Article  Google Scholar 

  94. Moskalenko, V.A., Entel, P., Dohotaru, L.A., Digor, D.F., et al., Diagrammatic theory for Anderson impurity model, Preprint E17-2008-56, Dubna: Joint Inst. Nuc-l. Res., 2008.

    Google Scholar 

  95. Moskalenko, V.A. and Perkins, N.B. The canonical transformation method in the periodic Anderson model, Theor. Math. Phys., 1999, vol. 121, no. 3, p. 1654. https://doi.org/10.1007/BF02557210

    Article  Google Scholar 

  96. Moskalenko, V.A., Entel P., Marinaro, M., Perkins, N.B., et al., Hopping perturbation treatment of the periodic Anderson model around the atomic limit, Phys. Rev. B, 2001, vol. 63, no. 24, p. 245119.

    Article  Google Scholar 

  97. Moskalenko, V.A., Perturbation theory for the periodic Anderson model, Theor. Math. Phys., 1997, vol. 110, p. 243. https://doi.org/10.1007/BF02630450

    Article  Google Scholar 

  98. Moskalenko, V.A., Perturbation theory for the periodic Anderson model: II. Superconducting state, Theor. Math. Phys., 1998, vol. 116, no. 3, p. 1094. https://doi.org/10.1007/BF02557150

    Article  Google Scholar 

  99. Medvedev, I.G., New diagram technique for the Anderson model, Theor. Math. Phys., 1996, vol. 109, no. 2, p. 1460. https://doi.org/10.1007/BF02072011

    Article  Google Scholar 

  100. Moskalenko, V.A., Entel, P., Digor, D.F., and Dohotaru, L.A., Competing spin waves and superconducting fluctuations in strongly correlated electron systems, Phase Trans., 2005, vol. 78, nos. 1–3, p. 277. https://doi.org/10.1080/01411590412331316519

    Article  Google Scholar 

  101. Pruschke, Th. and Bulla, R., Hund’s coupling and the metal-insulator transition in the two-band Hubbard model, Eur. Phys. J. B, 2005, vol. 44, p. 217. https://doi.org/10.1140/epjb/e2005-00117-4

    Article  Google Scholar 

  102. Didukh, L., Skorenkyy, Yu., Dovhopyaty, Yu., and Hankevych, V., Metal–insulator transition in a doubly orbitally degenerate model with correlated hopping, Phys. Rev. B, 2000, vol. 61, no. 12, p. 7893. https://doi.org/10.1103/PhysRevB.61.7893

    Article  Google Scholar 

  103. Koga, A., Imai, Y., and Kawakami, N., Stability of a metallic state in the two-orbital Hubbard model, Phys. Rev. B, 2002, vol. 66, no. 16, p. 165107. https://doi.org/10.1103/PhysRevB.66.165107

    Article  Google Scholar 

  104. Koga, A., Imai, Y., Suga, S.-I., and Kawakami, N., Effects of degenerate orbitals on the Hubbard model, J. Phys. Soc. Jpn., 2003, vol. 72, no. 5, p. 1306. https://doi.org/10.1143/JPSJ.72.1306

    Article  Google Scholar 

  105. Inaba, K. and Koga, A., Metal–insulator transition in the two-orbital Hubbard model at fractional band fillings: self-energy functional approach, J. Phys. Soc. Jpn., 2007, vol. 76, no. 9, p. 094712. https://doi.org/10.1143/JPSJ.76.094712

    Article  Google Scholar 

  106. Koga, A., Kawakami, N., Rice, T.M., and Sigrist, M., Mott transitions in the multi-orbital systems, Physica B: Condensed Matter, 2005, vols. 359–361, p. 1366. https://doi.org/10.1016/j.physb.2005.01.414

    Article  Google Scholar 

  107. Rong, Y. and Qimiao, Si., Mott transition in multiorbital models for iron pnictides, Phys. Rev. B, 2011, vol. 84, no. 24, p. 235115. https://doi.org/10.1103/PhysRevB.84.235115

    Article  Google Scholar 

  108. Lee, T.-H., Chubukov, A., Miao, H., and Kotliar, G., Pairing mechanism in Hund’s metal superconductors and the universality of the superconducting gap to critical temperature, Phys. Rev. Lett., 2018, vol. 121, no. 18, p. 187003. https://doi.org/10.1103/PhysRevLett.121.187003

    Article  Google Scholar 

  109. Nishikawa, Y. and Hewson, A.C., Study of Hund’s rule coupling in models of magnetic impurities and quantum dots, Phys. Rev. B, vol. 86, no. 24, p. 245131. https://doi.org/10.1103/PhysRevB.86.245131

  110. Kubo, K. and Hirashima, D.S., Effects of the Hund’s rule coupling in an orbitally degenerate Anderson model, J. Phys. Soc. Jpn., 1999, vol. 68, p. 2317. https://doi.org/10.1143/JPSJ.68.2317

    Article  Google Scholar 

  111. Fabrizio, M., Ho, A.F., De Leo, L., and Santoro, G.E., Nontrivial fixed point in a twofold orbitally degenerate Anderson impurity model, Phys. Rev. Lett., 2003, vol. 91, no. 24, p. 246402. https://doi.org/10.1103/PhysRevLett.91.246402

    Article  Google Scholar 

  112. De Leo, L. and Fabrizio, M., Spectral properties of a two-orbital Anderson impurity model across a non-Fermi-liquid fixed point, Phys. Rev. B, 2004, vol. 69, no. 24, p. 245114. https://doi.org/10.1103/PhysRevB.69.245114

    Article  Google Scholar 

  113. Kalra, M.L. and Upadhyaya, U.N., Role of the electron-phonon interaction in the insulator–metal transition, Nuov. Cim. B, 1977, vol. 41, no. 1, p. 151. https://doi.org/10.1007/BF02726550

    Article  Google Scholar 

  114. Tezuka, M., Arita, R. and Aoki, H., Phase diagram for the one-dimensional Hubbard–Holstein model: A density-matrix renormalization group study, Phys. Rev. B, 2007, vol. 76, no. 15, p. 155114. https://doi.org/10.1103/PhysRevB.76.155114

    Article  Google Scholar 

  115. Karakuzu, S., Luca, F., Tocchio, Sorella, S., et al., Superconductivity, charge-density waves, antiferromagnetism, and phase separation in the Hubbard–Holstein model, Phys. Rev. B, 2017, vol. 96, no. 20, p. 205145. https://doi.org/10.1103/PhysRevB.96.205145

    Article  Google Scholar 

  116. Yunkyu, B., Effects of phonon interaction on pairing in high-T c superconductors, Phys. Rev. B, 2008, vol. 78, no. 7, p. 075116. https://doi.org/10.1103/PhysRevB.78.075116

    Article  Google Scholar 

  117. Zimanyi, G.T., Kivelson, S.A., and Luther, A., Superconductivity from predominantly repulsive interactions in quasi one-dimensional systems, Phys. Rev. Lett., 1988, vol. 60, no. 20, p. 2089. https://doi.org/10.1103/PhysRevLett.60.2089

    Article  Google Scholar 

  118. Huang, W.-M., Shih, H.-Y., Wang, F., and Lin, H.-H., Anomalous isotope effect in phonon-dressed iron-based superconductor, Sci. Rep., 2019, vol. 9, p. 5547. https://doi.org/10.1038/s41598-019-42041-z

    Article  Google Scholar 

  119. Moskalenko, V.A., Electron–phonon interaction of strongly correlated systems. II. Strong coupling limit, Theor. Math. Phys., 1997, vol. 113, no. 3, p. 1559. https://doi.org/10.1007/BF0263451

    Article  Google Scholar 

  120. Moskalenko, V.A., Entel, P., and Digor, D.F., Strong interaction of correlated electrons with phonons: A diagrammatic approach, Phys. Rev. B, 1999, vol. 59, no. 1, p. 619. https://doi.org/10.1103/PhysRevB.59.619

    Article  Google Scholar 

  121. Moskalenko, V.A., Entel, P., and Digor, D.F., Strong interaction of correlated electrons with acoustical phonons using the extended Hubbard–Holstein model, Phys. Rev. B, 2006, vol. 74, no. 7, p. 075109. https://doi.org/10.1103/PhysRevB.74.075109

    Article  Google Scholar 

  122. Ramakumar, R. and Das, A.N., Polaron cross-overs and d-wave superconductivity in Hubbard–Holstein model, Eur. Phys. J. B, 2004, vol. 41, p. 197. https://doi.org/10.1140/epjb/e2004-00309

    Article  Google Scholar 

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The work was carried out within the framework of the project ANCD 20.80009.5007.07 (2020–2023) Tehnologii cuantice hibride advance (Advanced Quantum Hybrid Technologies).

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Chebotar’, I.D. Systems of Strongly Correlated Electrons Interacting with Each Other and with Phonons: Diagrammatic Approach. Surf. Engin. Appl.Electrochem. 60, 94–108 (2024). https://doi.org/10.3103/S1068375524010058

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