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The European Physical Journal Special Topics

, Volume 226, Issue 11, pp 2591–2613 | Cite as

Realistic many-body approaches to materials with strong nonlocal correlations

  • F. Lechermann
  • A. I. Lichtenstein
  • M. Potthoff
Open Access
Review
Part of the following topical collections:
  1. Dynamical Mean-Field Approach with Predictive Power for Strongly Correlated Materials

Abstract

Many of the fascinating and unconventional properties of several transition-metal compounds with partially filled d-shells are due to strong electronic correlations. While local correlations are in principle treated exactly within the frame of the dynamical mean-field theory, there are two major and interlinked routes for important further methodical advances: On the one hand, there is a strong need for methods being able to describe material-specific aspects, i.e., methods combining the DMFT with modern band-structure theory, and, on the other hand, nonlocal correlations beyond the mean-field paradigm must be accounted for. Referring to several concrete example systems, we argue why these two routes are worth pursuing and how they can be combined, we describe several related methodical developments and present respective results, and we discuss possible ways to overcome remaining obstacles.

References

  1. 1.
    P.M. Marcus, J.F. Janak, A.R. Williams, eds., Computational Methods in Band Theory (Plenum, New York, 1971)Google Scholar
  2. 2.
    O.K. Andersen, Phys. Rev. B 12, 3060 (1975)ADSCrossRefGoogle Scholar
  3. 3.
    P. Blaha, K. Schwarz, P. Sorantin, S.B. Trickey, Comput. Phys. Commun. 59, 399 (1990)ADSCrossRefGoogle Scholar
  4. 4.
    W.H. Butler, P.H. Dederichs, A. Gonis, R.L. Weaver, Applications of Multiple Scattering Theory to Material Science (Materials Reserach Society, Pittsburg Penn., 1992)Google Scholar
  5. 5.
    P. Hohenberg, W. Kohn, Phys. Rev. 136, 864 (1964)ADSMathSciNetCrossRefGoogle Scholar
  6. 6.
    W. Kohn, L.J. Sham, Phys. Rev. 140, 1133 (1965)ADSMathSciNetCrossRefGoogle Scholar
  7. 7.
    R.O. Jones, O. Gunnarsson, Rev. Mod. Phys. 61, 689 (1989)ADSCrossRefGoogle Scholar
  8. 8.
    M. Donath, P.A. Dowben, W. Nolting, eds., Magnetism and Electronic Correlations in Local-Moment Systems: Rare-earth Elements and Compounds (World Scientific, Singapore, 1998)Google Scholar
  9. 9.
    N.F. Mott, Metal-Insulator Transitions, 2nd edn. (Taylor and Francis, London, 1990)Google Scholar
  10. 10.
    J. Orenstein, A.J. Millis, Science 288, 468 (2000)ADSCrossRefGoogle Scholar
  11. 11.
    A.A. Abrikosow, L.P. Gorkov, I.E. Dzyaloshinski, Methods of Quantum Field Theory in Statistical Physics (Prentice-Hall, New Jersey, 1964)Google Scholar
  12. 12.
    S. Hüfner, ed., Very High Resolution Photoelectron Spectroscopy (Springer, New York, 2007)Google Scholar
  13. 13.
    M.C. Gutzwiller, Phys. Rev. Lett. 10, 159 (1963)ADSCrossRefGoogle Scholar
  14. 14.
    J. Hubbard, Proc. R. Soc. London A 276, 238 (1963)ADSCrossRefGoogle Scholar
  15. 15.
    J. Kanamori, Prog. Theor. Phys. (Kyoto) 30, 275 (1963)ADSCrossRefGoogle Scholar
  16. 16.
    W. Metzner, D. Vollhardt, Phys. Rev. Lett. 62, 324 (1989)ADSCrossRefGoogle Scholar
  17. 17.
    A. Georges, G. Kotliar, Phys. Rev. B 45, 6479 (1992)ADSCrossRefGoogle Scholar
  18. 18.
    A. Georges, G. Kotliar, W. Krauth, M.J. Rozenberg, Rev. Mod. Phys. 68, 13 (1996)ADSCrossRefGoogle Scholar
  19. 19.
    G. Kotliar, D. Vollhardt, Phys. Today 57, 53 (2004)CrossRefGoogle Scholar
  20. 20.
    M. Caffarel, W. Krauth, Phys. Rev. Lett. 72, 1545 (1994)ADSCrossRefGoogle Scholar
  21. 21.
    R. Bulla, T.A. Costi, T. Pruschke, Rev. Mod. Phys. 80, 395 (2008)ADSCrossRefGoogle Scholar
  22. 22.
    E. Gull, A. Millis, A. Lichtenstein, A. Rubtsov, M. Troyer, P. Werner, Rev. Mod. Phys. 83, 349 (2011)ADSCrossRefGoogle Scholar
  23. 23.
    M. Ganahl, P. Thunström, F. Verstraete, K. Held, H.G. Evertz, Phys. Rev. B 90, 045144 (2014)ADSCrossRefGoogle Scholar
  24. 24.
    Y. Lu, M. Höppner, O. Gunnarsson, M.W. Haverkort, Phys. Rev. B 90, 085102 (2014)ADSCrossRefGoogle Scholar
  25. 25.
    T. Maier, M. Jarrell, T. Pruschke, M.H. Hettler, Rev. Mod. Phys. 77, 1027 (2005)ADSCrossRefGoogle Scholar
  26. 26.
    A. Toschi, A.A. Katanin, K. Held, Phys. Rev. B 75, 045118 (2007)ADSCrossRefGoogle Scholar
  27. 27.
    A.N. Rubtsov, M.I. Katsnelson, A.I. Lichtenstein, Phys. Rev. B 77, 033101 (2008)ADSCrossRefGoogle Scholar
  28. 28.
    A.N. Rubtsov, M.I. Katsnelson, A.I. Lichtenstein, Ann. Phys. 327, 1320 (2012)ADSCrossRefGoogle Scholar
  29. 29.
    P.W. Anderson, Phys. Rev. 124, 41 (1961)ADSMathSciNetCrossRefGoogle Scholar
  30. 30.
    Z. Fisk, H. Ott, T.M. Rice, J. Smith, Nature 320, 124 (1986)ADSCrossRefGoogle Scholar
  31. 31.
    H. Tsunetsugu, M. Sigrist, K. Ueda, Rev. Mod. Phys. 69, 809 (1997)ADSCrossRefGoogle Scholar
  32. 32.
    S. Capponi, F.F. Assaad, Phys. Rev. B 63, 155114 (2001)ADSCrossRefGoogle Scholar
  33. 33.
    J.R. Schrieffer, P.A. Wolff, Phys. Rev. 149, 491 (1966)ADSCrossRefGoogle Scholar
  34. 34.
    S. Doniach, Physica 91B, 321 (1977)Google Scholar
  35. 35.
    H.v. Löhneysen, A. Rosch, M. Vojta, P. Wölfle, Rev. Mod. Phys. 79, 1015 (2007)ADSCrossRefGoogle Scholar
  36. 36.
    M.A. Ruderman, C. Kittel, Phys. Rev. 96, 99 (1954)ADSCrossRefGoogle Scholar
  37. 37.
    J. Kondo, Prog. Theor. Phys. 32, 37 (1964)ADSCrossRefGoogle Scholar
  38. 38.
    A.C. Hewson, The Kondo Problem to Heavy Fermions, Cambridge Studies in Magnetism (Cambridge Universiy Press, Cambridge, 1997)Google Scholar
  39. 39.
    M.W. Aulbach, F.F. Assaad, M. Potthoff, Phys. Rev. B 92, 235131 (2015)ADSCrossRefGoogle Scholar
  40. 40.
    A.N. Rubtsov, V.V. Savkin, A.I. Lichtenstein, Phys. Rev. B 72, 035122 (2005)ADSCrossRefGoogle Scholar
  41. 41.
    P. Werner, A. Comanac, L. de’ Medici, M. Troyer, A.J. Millis, Phys. Rev. Lett. 97, 076405 (2006)ADSCrossRefGoogle Scholar
  42. 42.
    Y. Motome, K. Nakamikawa, Y. Yamaji, M. Udagawa, Phys. Rev. Lett. 105, 036403 (2010)ADSCrossRefGoogle Scholar
  43. 43.
    R. Ballou, C. Lacroix, M.D. Nunez Regueiro, Phys. Rev. Lett. 66, 1910 (1991)ADSCrossRefGoogle Scholar
  44. 44.
    A. Benlagra, L. Fritz, M. Vojta, Phys. Rev. B 84, 075126 (2011)ADSCrossRefGoogle Scholar
  45. 45.
    S. Hayami, M. Udagawa, Y. Motome, J. Phys. Soc. Jpn. 80, 073704 (2011)ADSCrossRefGoogle Scholar
  46. 46.
    S. Hayami, M. Udagawa, Y. Motome, J. Phys. Soc. Jpn. 81, 103707 (2012)ADSCrossRefGoogle Scholar
  47. 47.
    M. Potthoff, W. Nolting, Phys. Rev. B 55, 2741 (1997)ADSCrossRefGoogle Scholar
  48. 48.
    I. Titvinidze, A. Schwabe, N. Rother, M. Potthoff, Phys. Rev. B 86, 075141 (2012)ADSCrossRefGoogle Scholar
  49. 49.
    M.W. Aulbach, I. Titvinidze, M. Potthoff, Phys. Rev. B 91, 174420 (2015)ADSCrossRefGoogle Scholar
  50. 50.
    G. Kotliar, S.Y. Savrasov, K. Haule, V.S. Oudovenko, O. Parcollet, C.A. Marianetti, Rev. Mod. Phys. 78, 865 (2006)ADSCrossRefGoogle Scholar
  51. 51.
    S. Biermann, F. Aryasetiawan, A. Georges, Phys. Rev. Lett. 90, 086402 (2003)ADSCrossRefGoogle Scholar
  52. 52.
    P. Sun, G. Kotliar, Phys. Rev. B 66, 085120 (2002)ADSCrossRefGoogle Scholar
  53. 53.
    E.G.C.P. van Loon, H. Hafermann, A.I. Lichtenstein, A.N. Rubtsov, M.I. Katsnelson, Phys. Rev. Lett. 113, 246407 (2014)ADSCrossRefGoogle Scholar
  54. 54.
    E.A. Stepanov, E.G.C.P. van Loon, A.A. Katanin, A.I. Lichtenstein, M.I. Katsnelson, A.N. Rubtsov, Phys. Rev. B 93, 045107 (2016)ADSCrossRefGoogle Scholar
  55. 55.
    V.I. Anisimov, A.I. Poteryaev, M.A. Korotin, A.O. Anokhin, G. Kotliar, J. Phys.: Condens. Matter 9, 7359 (1997)ADSGoogle Scholar
  56. 56.
    A.I. Lichtenstein, M. Katsnelson, Phys. Rev. B 57, 6884 (1998)ADSCrossRefGoogle Scholar
  57. 57.
    J. Minár, L. Chioncel, A. Perlov, H. Ebert, M.I. Katsnelson, A.I. Lichtenstein, Phys. Rev. B 72, 045125 (2005)ADSCrossRefGoogle Scholar
  58. 58.
    N. Marzari, A.A. Mostofi, J.R. Yates, I. Souza, D. Vanderbilt, Rev. Mod. Phys. 84, 1419 (2012)ADSCrossRefGoogle Scholar
  59. 59.
    F. Lechermann, A. Georges, A. Poteryaev, S. Biermann, M. Posternak, A. Yamasaki, O.K. Andersen, Phys. Rev. B 74, 125120 (2006)ADSCrossRefGoogle Scholar
  60. 60.
    B. Amadon, F. Lechermann, A. Georges, F. Jollet, T.O. Wehling, A.I. Lichtenstein, Phys. Rev. B 77, 205112 (2008)ADSCrossRefGoogle Scholar
  61. 61.
    V.I. Anisimov, D.E. Kondakov, A.V. Kozhevnikov, I.A. Nekrasov, Z.V. Pchelkina, J.W. Allen, S.K. Mo, H.D. Kim, P. Metcalf, S. Suga, et al., Phys. Rev. B 71, 125119 (2005)ADSCrossRefGoogle Scholar
  62. 62.
    K. Held, G. Keller, V. Eyert, D. Vollhardt, V.I. Anisimov, Phys. Rev. Lett. 86, 5345 (2001)ADSCrossRefGoogle Scholar
  63. 63.
    A.I. Lichtenstein, M. Katsnelson, G. Kotliar, Phys. Rev. Lett. 87, 067205 (2001)ADSCrossRefGoogle Scholar
  64. 64.
    E. Pavarini, S. Biermann, A. Poteryaev, A.I. Lichtenstein, A. Georges, O.K. Andersen, Phys. Rev. Lett. 92, 176403 (2004)ADSCrossRefGoogle Scholar
  65. 65.
    S.Y. Savrasov, G. Kotliar, E. Abrahams, Nature 410, 793 (2001)ADSCrossRefGoogle Scholar
  66. 66.
    L.V. Pourovskii, B. Amadon, S. Biermann, A. Georges, Phys. Rev. B 76, 235101 (2007)ADSCrossRefGoogle Scholar
  67. 67.
    D. Grieger, C. Piefke, O.E. Peil, F. Lechermann, Phys. Rev. B 86, 155121 (2012)ADSCrossRefGoogle Scholar
  68. 68.
    V.I. Anisimov, J. Zaanen, O.K. Andersen, Phys. Rev. B 44, 943 (1991)ADSCrossRefGoogle Scholar
  69. 69.
    V.I. Anisimov, I.V. Solovyev, M.A. Korotin, M.T. Czyżyk, G.A. Sawatzky, Phys. Rev. B 48, 16929 (1993)ADSCrossRefGoogle Scholar
  70. 70.
    M.T. Czyżyk, G.A. Sawatzky, Phys. Rev. B 49, 14211 (1994)ADSCrossRefGoogle Scholar
  71. 71.
    A. Georges, Strongly Correlated Electron Materials: Dynamical mean-field Theory and Electronic Structure, Lectures on the Physics of Highly Correlated Electron Systems VIII, AIP Conf. Proc. 715, 3 (2004)ADSGoogle Scholar
  72. 72.
    F. Lechermann, L. Boehnke, D. Grieger, C. Piefke, Phys. Rev. B 90, 085125 (2014)ADSCrossRefGoogle Scholar
  73. 73.
    D. Grieger, F. Lechermann, Phys. Rev. B 90, 115115 (2014)ADSCrossRefGoogle Scholar
  74. 74.
    S.G. Louie, K.M. Ho, M.L. Cohen, Phys. Rev. B 19, 1774 (1979)ADSCrossRefGoogle Scholar
  75. 75.
    O. Parcollet, M. Ferrero, T. Ayral, H. Hafermann, I. Krivenko, L. Messio, P. Seth, Comput. Phys. Commun. 196, 398 (2015)ADSCrossRefGoogle Scholar
  76. 76.
    P. Seth, I. Krivenko, M. Ferrero, O. Parcollet, Comput. Phys. Commun. 200, 274 (2016)ADSCrossRefGoogle Scholar
  77. 77.
    C. Castellani, C.R. Natoli, J. Ranninger, Phys. Rev. B 18, 4945 (1978)ADSCrossRefGoogle Scholar
  78. 78.
    D.B. McWhan, T.M. Rice, J.B. Remeika, Phys. Rev. Lett. 23, 1384 (1969)ADSCrossRefGoogle Scholar
  79. 79.
    D.B. McWhan, J.B. Remeika, T.M. Rice, W.F. Brinkman, J.P. Maita, A. Menth, Phys. Rev. Lett. 27, 941 (1971)ADSCrossRefGoogle Scholar
  80. 80.
    A.E. Antipov, I.S. Krivenko, V.I. Anisimov, A.I. Lichtenstein, A.N. Rubtsov, Phys. Rev. B 86, 155107 (2012)ADSCrossRefGoogle Scholar
  81. 81.
    P.D. Dernier, J. Phys. Chem. Solids 31, 2569 (1970)ADSCrossRefGoogle Scholar
  82. 82.
    J.H. Park, L.H. Tjeng, A. Tanaka, J.W. Allen, C.T. Chen, P. Metcalf, J.M. Honig, F.M.F. de Groot, G.A. Sawatzky, Phys. Rev. B 61, 11506 (2000)ADSCrossRefGoogle Scholar
  83. 83.
    L.F. Mattheiss, J. Phys.: Condens. Matter 6, 6477 (1994)ADSGoogle Scholar
  84. 84.
    S.Y. Ezhov, V.I. Anisimov, D.I. Khomskii, G.A. Sawatzky, Phys. Rev. Lett. 83, 4136 (1999)ADSCrossRefGoogle Scholar
  85. 85.
    I.S. Elfimov, T. Saha-Dasgupta, M.A. Korotin, Phys. Rev. B 68, 113105 (2003)ADSCrossRefGoogle Scholar
  86. 86.
    V. Eyert, U. Schwingenschlögl, U. Eckern, Europhys. Lett. 70, 782 (2005)ADSCrossRefGoogle Scholar
  87. 87.
    Y. Guo, S.J. Clark, J. Robertson, J. Chem. Phys. 140 (2014)Google Scholar
  88. 88.
    G. Keller, K. Held, V. Eyert, D. Vollhardt, V.I. Anisimov, Phys. Rev. B 70, 205116 (2004)ADSCrossRefGoogle Scholar
  89. 89.
    A.I. Poteryaev, J.M. Tomczak, S. Biermann, A. Georges, A.I. Lichtenstein, A.N. Rubtsov, T. Saha-Dasgupta, O.K. Andersen, Phys. Rev. B 76, 085127 (2007)ADSCrossRefGoogle Scholar
  90. 90.
    M. Sandri, M. Capone, M. Fabrizio, Phys. Rev. B 87, 205108 (2013)ADSCrossRefGoogle Scholar
  91. 91.
    X. Deng, A. Sternbach, K. Haule, D. Basov, G. Kotliar, Phys. Rev. Lett. 113, 246404 (2014)ADSCrossRefGoogle Scholar
  92. 92.
    I. Leonov, V.I. Anisimov, D. Vollhardt, Phys. Rev. B 91, 195115 (2015)ADSCrossRefGoogle Scholar
  93. 93.
    I. Lo Vecchio, J.D. Denlinger, O. Krupin, B.J. Kim, P.A. Metcalf, S. Lupi, J.W. Allen, A. Lanzara, Phys. Rev. Lett. 117, 166401 (2016)ADSCrossRefGoogle Scholar
  94. 94.
    S.R. Hassan, A. Georges, H.R. Krishnamurthy, Phys. Rev. Lett. 94, 036402 (2005)ADSCrossRefGoogle Scholar
  95. 95.
    F. Rodolakis, J.P. Rueff, M. Sikora, I. Alliot, J.P. Itié, F. Baudelet, S. Ravy, P. Wzietek, P. Hansmann, A. Toschi, et al., Phys. Rev. B 84, 245113 (2011)ADSCrossRefGoogle Scholar
  96. 96.
    P. Zubko, S. Gariglio, M. Gabay, P. Ghosez, J.M. Triscone, Annu. Rev. Condens. Matter Phys. 2, 141 (2011)ADSCrossRefGoogle Scholar
  97. 97.
    H.Y. Hwang, Y. Iwasa, M. Kawasaki, B. Keimer, N. Nagaosa, Y. Tokura, Nat. Mater. 11, 103 (2012)ADSCrossRefGoogle Scholar
  98. 98.
    J. Chakhalian, J.W. Freeland, A.J. Millis, C. Panagopoulos, J.M. Rondinelli, Rev. Mod. Phys. 86, 1189 (2014)ADSCrossRefGoogle Scholar
  99. 99.
    C.A. Jackson, J.Y. Zhang, C.R. Freeze, S. Stemmer, Nat. Commun. 5, 4258 (2014)ADSCrossRefGoogle Scholar
  100. 100.
    R. Chen, S.B. Lee, L. Balents, Phys. Rev. B 87, 161119(R) (2013)ADSCrossRefGoogle Scholar
  101. 101.
    F. Lechermann, M. Obermeyer, New J. Phys. 17, 043026 (2015)ADSCrossRefGoogle Scholar
  102. 102.
    A.C. Komarek, H. Roth, M. Cwik, W.D. Stein, J. Baier, M. Kriener, F. Bourée, T. Lorenz, M. Braden, Phys. Rev. B 75, 224402 (2007)ADSCrossRefGoogle Scholar
  103. 103.
    F. Lechermann, arXiv:1603.01031 (2016)
  104. 104.
    L. Boehnke, F. Lechermann, Phys. Rev. B 85, 115128 (2012)ADSCrossRefGoogle Scholar
  105. 105.
    A. Wilhelm, F. Lechermann, H. Hafermann, et al., Phys. Rev. B 91, 155114 (2015)ADSCrossRefGoogle Scholar
  106. 106.
    H. Ohta, K. Yoshimura, Z. Hu, Y.Y. Chin, H.J. Lin, H.H. Hsieh, C.T. Chen, L.H. Tjeng, Phys. Rev. Lett. 107, 066404 (2011)ADSCrossRefGoogle Scholar
  107. 107.
    L. Boehnke, H. Hafermann, M. Ferrero, F. Lechermann, O. Parcollet, Phys. Rev. B 84, 075145 (2011)ADSCrossRefGoogle Scholar
  108. 108.
    N.L. Wang, P. Zheng, D. Wu, Y.C. Ma, T. Xiang, R.Y. Jin, D. Mandrus, Phys. Rev. Lett. 93, 237007 (2004)ADSCrossRefGoogle Scholar
  109. 109.
    U. Schollwöck, Ann. Phys. (N.Y.) 326, 96 (2011)ADSMathSciNetCrossRefGoogle Scholar
  110. 110.
    J. Braun, R. Rausch, M. Potthoff, J. Minar, H. Ebert, Phys. Rev. B 91, 035119 (2015)ADSCrossRefGoogle Scholar
  111. 111.
    H. Aoki, N. Tsuji, M. Eckstein, M. Kollar, T. Oka, P. Werner, Rev. Mod. Phys. 86, 779 (2014)ADSCrossRefGoogle Scholar
  112. 112.
    Y. Ge, J. Eisert, New J. Phys. 18, 083026 (2016)ADSCrossRefGoogle Scholar
  113. 113.
    P.E. Blöchl, T. Pruschke, M. Potthoff, Phys. Rev. B 88, 205139 (2013)ADSCrossRefGoogle Scholar

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Authors and Affiliations

  • F. Lechermann
    • 1
    • 2
  • A. I. Lichtenstein
    • 1
  • M. Potthoff
    • 1
  1. 1.I. Institut für Theoretische Physik, Universität HamburgHamburgGermany
  2. 2.Institut für Keramische Hochleistungswerkstoffe, Technische Universität Hamburg-HarburgHamburgGermany

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