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.
REFERENCES
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
Schubin, S.P. and Wonsowskii, S.V., On the electron theory of metals, Proc. R. Soc., 1934, vol. A145, no. 854, p. 159.
Schubin, S. and Vonsowsky, S., Zur Elektronentheorie der Metalle I, Phys. Zs. UdSSR, 1935, vol. 7, no. 1, p. 292.
Schubin, S. and Vonsowsky, S., Zur Elektronentheorie der Metalle II, Phys. Zs. UdSSR, 1936, vol. 10, no. 3, p. 348.
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.
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.
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
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
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
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
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
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
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
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
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)
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
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
Franck, J.P., Physical Properties of High Temperature Superconductors IV, Ginsberg, D.M., Ed., Singapore: World Scientific, 1994, p. 189.
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
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
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
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
Alexandrov, A.S. and Krebs, A.B., Polarons in high-temperature superconductors, Sov. Phys. Usp., 1992, vol. 35, no. 5, p. 345.
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
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.
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
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.
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.
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
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.
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
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
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
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
Mott, N.F., The transition to the metallic state, Philos. Mag., 1961, vol. 6, no. 62, p. 287. https://doi.org/10.1080/14786436108243318
Mott, N.F., Metal–Insulator Transitions, Taylor and Francis, 1974.
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
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
Stewart, G.R., Heavy-fermion systems, Rev. Mod. Phys., 1984, vol. 56, no. 4, p. 755. https://doi.org/10.1103/RevModPhys.56.755
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
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
Putilin, S.N., Antipov, E.V., Chmaissem, O., and Marezio, M., Superconductivity at 94 K in HgBa2CuO4+δ, Nature, 1993, vol. 362, p. 226.
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.
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
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
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
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
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
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
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
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
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
Bogoliubov, N.N., A new method in the theory of superconductivity. I, Sov. Phys. JETP, 1958, vol. 34, p. 41.
Gor’kov, L.P, On the energy spectrum of superconductors, Sov. Phys. JETP, 1958, vol. 7, no. 3, p. 505.
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.
Moskalenko, V.A., Superconductivity of metals taking into account the overlap of energy bands, Fiz. Metal. Metalloved., 1959, vol. 8, no. 4, p. 503.
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
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
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
Scalapino, D.J., Superconductivity and spin fluctuations, J. Low Temp. Phys., 1999, vol. 117, no. p. 179. https://doi.org/10.1023/A:1022559920049
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
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
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
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
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
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
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
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
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
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
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
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
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
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.
Izyumov, Yu.A. and Kassan-ogly, F.L., Polevyye metody v teorii ferromagnetizma (Field Methods in the Theory of Ferromagnetism), Moscow: Nauka, 1974.
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
Zaitsev, R.O., Generalized diagram technique and spin waves in an anisotropic ferromagnet, Sov. Phys. JETP, 1976, vol. 41, no. 3, p. 100.
Izyumov, Yu.A., Katsnel’son, M.I., Skryabin, Yu.N., Magnetizm kollektivizirovannykh elektronov (Magnetism of Itinerant Electrons), Moscow: Fizmatlit, 1994.
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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.
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.
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
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.
Moskalenko, V.A., Perturbation theory for the periodic Anderson model, Theor. Math. Phys., 1997, vol. 110, p. 243. https://doi.org/10.1007/BF02630450
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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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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DOI: https://doi.org/10.3103/S1068375524010058