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Reviews of topical problems


Hubbard model of strong correlations


Mikheev Institute of Metal Physics, Ural Division of the Russian Academy of Sciences, S Kovalevskoi str. 18, Ekaterinburg, 620108, Russian Federation

A state-of-the-art review is given of the investigations of the Hubbard model, which is the main model used in the theory of strongly correlated electron systems. It is shown how the main correlation effects — the metal-insulator phase transition, the appearance of localised magnetic moments, and the breakdown of the Fermi-liquid behaviour — appear in the case of strong electron correlations when U ~ W, where U is the Coulomb repulsion parameter and W is the band width. Different approaches to the problem, not based on perturbation theory in terms of the parameter U/W or W/U, are presented. A new method in the theory of strongly correlated systems, in which the limit of infinite number of dimensions of space, d = infty, is the main feature of the review. The physical results obtained by this approach are compared with those deduced by traditional methods. An overview of the behaviour of strongly correlated systems is given for wide ranges of the model parameters U and W, and of the electron density n.

Fulltext pdf (660 KB)
Fulltext is also available at DOI: 10.1070/PU1995v038n04ABEH000081
PACS: 71.27.+a
DOI: 10.1070/PU1995v038n04ABEH000081
URL: https://ufn.ru/en/articles/1995/4/b/
A1995RH54700002
Citation: Izyumov Yu A "Hubbard model of strong correlations" Phys. Usp. 38 385–408 (1995)
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Оригинал: Изюмов Ю А «Модель Хаббарда в режиме сильных корреляций» УФН 165 403–427 (1995); DOI: 10.3367/UFNr.0165.199504b.0403

References (112) ↓ Cited by (76) Similar articles (20)

  1. Hubbard J Proc. R. Soc. London A 276 238 (1963)
  2. Gutzwiller M C Phys. Rev. Lett. 10 159 (1963)
  3. Kanamori J Prog. Theor. Phys. 30 275 (1963)
  4. Anderson P W Phys. Rev. 124 41 (1961)
  5. Shubin S P, Wonsowsky S V Proc. R. Soc. London A 145 159 (1934)
  6. Izyumov Yu A Usp. Fiz. Nauk 161 (11) 1 (1991); Izyumov Yu A Sov. Phys. Usp. 34 935 (1991)
  7. Izuyama T, Kim D, Kubo R J. Phys. Soc. Jpn. Vol. 18 (1963) p. 1025
  8. Penn D R Phys. Rev. 142 350 (1966)
  9. Moriya R Spin Fluctuations In Itinerant Electron Magnetism (Berlin: Springer, 1985)
  10. Chao K A, Spalek J, Oles A M J. Phys. C 10 L271 (1977)
  11. Izyumov Yu A, Letfulov B M J. Phys. Condens. Matter 2 8905 (1990)
  12. Izyumov Yu A, Letfulov B M, Shipitsyn E V J. Phys. Condens. Matter 4 9951 (1992)
  13. Izyumov Yu A, Letfulov B M, Shipitsin E V Zh. Eksp. Teor. Fiz. 105 1357 (1994); Izyumov Yu A, Letfulov B M, Shipitsin E V JETP 78 731 (1994)
  14. Hubbard J Proc. R. Soc. London A 281 401 (1964)
  15. Mott N F Philos. Mag. 6 287 (1961)
  16. Metzner W, Vollhardt D Phys. Rev. Lett. 62 324 (1989)
  17. Hubbard J Phys. Rev. B 19 2626 (1979); Hubbard J Phys. Rev. B 20 4584 (1979); Hubbard J Phys. Rev. B 23 5974 (1981)
  18. Hasegawa H J. Phys. Soc. Jpn. 46 1504 (1979); Hasegawa H J. Phys. Soc. Jpn. 49 178 (1980)
  19. Gutzwiller M C Phys. Rev. A 137 1726 (1965)
  20. Bogolyubov N N, Tyablikov S V Dokl. Akad. Nauk SSSR R 126 53 (1959); Bogolyubov N N, Tyablikov S V Sov. Phys. Dokl. 4 589 (1959)
  21. Zubarev D N Usp. Fiz. Nauk 71 71 (1960); Zubarev D N Sov. Phys. Usp. 3 320 (1960)
  22. Zaitsev R O Zh. Eksp. Teor. Fiz. 70 1100 (1976); Zaitsev R O Sov. Phys. JETP 43 574 (1976); Zaitsev R O Zh. Eksp. Teor. Fiz. 75 2362 (1978); Zaitsev R O Sov. Phys. JETP 48 1193 (1978)
  23. Goryachev E G, Kuzmin E V, Ovchinnikov S G J. Phys. C 15 1481 (1982)
  24. Izyumov Yu A, Skryabin Yu N Statisticheskaya Mekhanika Magnitouporyadochennykh Sistem (M.: Nauka, 1987)
  25. Ehrenreich H, Schwartz L M Solid State Phys. 31 150 (1976)
  26. Arai T, Cohen M H Phys. Rev. B 15 1836 (1977); Arai T, Cohen M H Phys. Rev. B 21 3300 (1980); Arai T, Cohen M H Phys. Rev. B 21 3309 (1980)
  27. Anokhin A O, Irkhin V Yu Phys. Status Solidi B 165 129 (1991)
  28. Anokhin A O, Irkhin V Yu, Katsnelson M I J. Phys. Condens. Matter 3 1475 (1991)
  29. Muller-Hartmann E Solid State Commun. 12 1269 (1973)
  30. Muller-Hartmann E Z. Phys. B 76 211 (1989)
  31. Brandt U, Meilsch C Z. Phys. B 75 365 (1989); Brandt U, Meilsch C Z. Phys. 79 295 (1990)
  32. Velicky B, Kirkpatrick S, Ehrenreich H Phys. Rev. 175 747 (1968)
  33. Vollhardt D Proc. Int. School o f Physics "Enrico Fermi" Course CXXI Eds R A Broglia, J R Schrieffer (Amsterdam: North-Holland, 1994) p. 31
  34. Georges A, Kotliar G Phys. Rev. B 45 6479 (1992)
  35. Jarrell M Phys. Rev. Lett. 69 168 (1992)
  36. Janis V, Vollhardt D Int. J. Mod. Phys. B 6 731 (1992)
  37. Wolff P A Phys. Rev. 124 1030 (1961)
  38. Haldane F D M Phys. Rev. Lett. 40 416 (1978)
  39. Georges A, Kotliar G, Si Q Int. J. Mod. Phys. B 6 705 (1992)
  40. Georges A, Krauth W Phys. Rev. Lett. 69 1240 (1992)
  41. Rozenberg M J, Zhang X Y, Kotliar G Phys. Rev. Lett. 69 1236 (1992)
  42. Zhang X Y, Rozenberg M J, Kotliar G Phys. Rev. Lett. 70 1666 (1993)
  43. Pruschke T, Cox D L, Jarrell M Phys. Rev. B 47 3553 (1993)
  44. Jarrell M, Pruschke T Z. Phys. B 90 187 (1993)
  45. Scalettar R T, Scalapino D J, Sugar R L, Toussaint D Phys. Rev. B 39 4711 (1989)
  46. Leib E H, Wu F Y Phys. Rev. Lett. 20 1445 (1968)
  47. Frahm H, Korepin V E Phys. Rev. B 42 10553 (1990)
  48. Edwards D M, Hertz J A Physica B 163 527 (1990)
  49. Wermbter S, Czycholl G "Metal-Insulator transition and fermi-liquid behaviour on the infinite dimensional Hubbard model" Report No. 58 (Universitat Bremen, 1994)
  50. Edwards D M J. Phys. Condens. Matter 5 161 (1993)
  51. Baym G, Kadanoff L P Phys. Rev. 124 287 (1961)
  52. Baym G Phys. Rev. 127 1391 (1962)
  53. Schweitzer H, Czycholl G Z. Phys. B 79 377 (1990)
  54. Janis V Z. Phys. B 83 227 (1991)
  55. van Dongen P G J Phys. Rev. Lett. 67 757 (1991)
  56. van Dongen P G J, Vollhardt D Phys. Rev. Lett. 65 1663 (1990)
  57. Ohkawa F J J. Phys. Soc. Jpn. 61 1615 (1992)
  58. Dobrosavljevic V, Kotliar G Phys. Rev. B 50 1430 (1994)
  59. Hirsch J E, Fye R M Phys. Rev. Lett. 56 2521 (1986)
  60. Zlatic V, Horvatic B Phys. Rev. B 28 6904 (1983)
  61. Menge B, Muller-Hartmann E Z. Phys. B 82 237 (1991)
  62. Cyrot M J. Physique 33 125 (1972)
  63. Takahashi Y J. Phys. Soc. Jpn. 55 3553 (1986)
  64. Kakehashi Y, Fulde P Phys. Rev. B 32 1595 (1985)
  65. Kakehashi Y, Hasegawa H Phys. Rev. B 37 7777 (1988)
  66. Schrieffer J R, Evenson W E, Wang S Q J. Physique 32 C1 (1971)
  67. Hertz J A, Klenin M A Phys. Rev. B 10 1084 (1974)
  68. Yokoyama H, Shiba H J. Phys. Soc. Jpn. 56 3582 (1987)
  69. Hirsch J E Phys. Rev. B 35 1851 (1987)
  70. Kakehashi Y, Samson J H Phys. Rev. B 33 298 (1986)
  71. Vollhardt D Rev. Mod. Phys. 56 99 (1984)
  72. Metzner W, Vollhardt D Phys. Rev. Lett. 62 324 (1989)
  73. Metzner W Z. Phys. B 77 253 (1989)
  74. Vollhardt D, van Dongen P G J, Gebhard F, Metzner W Mod. Phys. Lett. 4 499 (1990)
  75. van Dongen P G J, Gebhard F, Vollhardt D Z. Phys. B 76 199 (1989)
  76. Gebhard F Phys. Rev. B 41 9452 (1990)
  77. Fazekas P, Menge B, Muller-Hartmann E Z. Phys. B 78 69 (1990)
  78. Nagaev E L Fizika Magnitnykh Poluprovodnikov (M.: Nauka, 1979)
  79. Visscher P B Phys. Rev. B 10 943 (1974)
  80. Ogawa T, Kanda K, Matsubara K Prog. Theor. Phys. 53 614 (1975)
  81. Florencio J Jr, Chao K A Phys. Rev. B 14 3121 (1976)
  82. Ioffe L B, Larkin A I Phys. Rev. B 39 8988 (1989)
  83. Shastry B S, Krishnamurthy H R, Anderson P W Phys. Rev. B 41 2375 (1990)
  84. van der Linden W, Edwards D M J. Phys. Condens. Matter 3 4917 (1991)
  85. Hubbard J Proc. R. Soc. London A 285 542 (1965); Hubbard J Proc. R. Soc. London A 296 82 (1966)
  86. Zaitsev R O Zh. Eksp. Teor. Fiz. 68 207 (1975); Zaitsev R O Sov. Phys. JETP 41 100 (1975); Zaitsev R O Zh. Eksp. Teor. Fiz. 70 1100 (1976); Zaitsev R O Sov. Phys. JETP 43 574 (1976)
  87. Barnes S E J. Phys. F 6 1375 (1976)
  88. Coleman P Phys. Rev. B 29 3035 (1984)
  89. Zou Z, Anderson P W Phys. Rev. B 37 627 (1988)
  90. Kotliar G, Ruckenstein A E Phys. Rev. Lett. 57 1362 (1986)
  91. Kane C L, Lett P A, Read N Phys. Rev. B 39 6880 (1989)
  92. Nagaosa N, Lee P A Phys. Rev. Lett. 64 2450 (1990); Lee P A, Nagaosa N Phys. Rev. B 46 5621
  93. Fresard R, Wolfle P Int. J. Mod. Phys. B 6 685 (1992)
  94. Grilli M, Kotliar G Phys. Rev. Lett. 64 1170 (1990)
  95. Arovas D P, Auerbach A Phys. Rev. B 38 316 (1988)
  96. Feng S, Wu J B, Su Z B, Yu L Phys. Rev. B 47 15192 (1993)
  97. Tanamoto T, Kuboki K, Fukuyama H J. Phys. Soc. Jpn. 60 3072 (1991)
  98. Markelov A V Mod. Phys. Lett. B 6 1181 (1992)
  99. Khaliullin G G Pis’ma ZhETF 52 999 (1990); Khaliullin G G JETP Lett. 52 389 (1990)
  100. Wang Y R, Rice M J Phys. Rev. B 49 4360 (1994)
  101. van Dongen P G J, Janis V Phys. Rev. Lett. 72 3258 (1994)
  102. Janis V Phys. Rev. B 49 1612 (1994)
  103. Jarrell M, Pruschke T Phys. Rev. B 49 1458 (1994)
  104. Zhang X Y, Zhang G M Phys. Rev. B 49 7929 (1994)
  105. Rozenberg M J, Kotliar G, Zhang X Y Phys. Rev. B 49 10181 (1994)
  106. Li Y M, d’Anbrumenil N Phys. Rev. B 49 6058 (1994)
  107. Metzner W, Schmit P, Vollhardt D Phys. Rev. B 45 2237 (1992)
  108. Strack R, Vollhardt D Phys. Rev. B 46 13852 (1992)
  109. Czycholl G, Schweitzer H Phys. Scr. T-45 125 (1992)
  110. van Dongen P G J Phys. Rev. Lett. 67 757 (1991)
  111. Si Q, Kotliar G Phys. Rev. B 48 13881 (1993)
  112. Si Q, Kotliar G Phys. Rev. Lett. 70 3143 (1993)

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