The European Physical Journal Special Topics

, Volume 226, Issue 11, pp 2641–2675 | Cite as

LDA+DMFT approach to ordering phenomena and the structural stability of correlated materials

  • J. Kuneš
  • I. Leonov
  • P. Augustinský
  • V. Křápek
  • M. Kollar
  • D. Vollhardt
Open Access
Part of the following topical collections:
  1. Dynamical Mean-Field Approach with Predictive Power for Strongly Correlated Materials


Materials with correlated electrons often respond very strongly to external or internal influences, leading to instabilities and states of matter with broken symmetry. This behavior can be studied theoretically either by evaluating the linear response characteristics, or by simulating the ordered phases of the materials under investigation. We developed the necessary tools within the dynamical mean-field theory (DMFT) to search for electronic instabilities in materials close to spin-state crossovers and to analyze the properties of the corresponding ordered states. This investigation, motivated by the physics of LaCoO3, led to a discovery of condensation of spinful excitons in the two-orbital Hubbard model with a surprisingly rich phase diagram. The results are reviewed in the first part of the article. Electronic correlations can also be the driving force behind structural transformations of materials. To be able to investigate correlation-induced phase instabilities we developed and implemented a formalism for the computation of total energies and forces within a fully charge self-consistent combination of density functional theory and DMFT. Applications of this scheme to the study of structural instabilities of selected correlated electron materials such as Fe and FeSe are reviewed in the second part of the paper.


  1. 1.
    M. Imada, A. Fujimori, Y. Tokura, Rev. Mod. Phys. 70, 1039 (1998)ADSCrossRefGoogle Scholar
  2. 2.
    Y. Tokura, N. Nagaosa, Science 288, 462 (2000)ADSCrossRefGoogle Scholar
  3. 3.
    E. Dagotto, Science 309, 257 (2005)ADSCrossRefGoogle Scholar
  4. 4.
    R.O. Jones, O. Gunnarsson, Rev. Mod. Phys. 61, 689 (1989)ADSCrossRefGoogle Scholar
  5. 5.
    J.P. Perdew, K. Burke, M. Ernzerhof, Phys. Rev. Lett. 77, 3865 (1996)ADSCrossRefGoogle Scholar
  6. 6.
    V.I. Anisimov, J. Zaanen, O.K. Andersen, Phys. Rev. B 44, 943 (1991)ADSCrossRefGoogle Scholar
  7. 7.
    S. Baroni, S. de Gironcoli, A.D. Corso, P. Giannozzi, Rev. Mod. Phys. 73, 515 (2001)ADSCrossRefGoogle Scholar
  8. 8.
    P. Blaha, K. Schwarz, G. Madsen, D. Kvasnicka, J. Luitz, WIEN2k, An Augmented Plane Wave + Local Orbitals Program for Calculating Crystal Properties (Karlheinz Schwarz, Techn. Universität Wien, Austria, 2001)Google Scholar
  9. 9.
    G. Kresse, J. Hafner, Phys. Rev. B 47, 558 (1993)ADSCrossRefGoogle Scholar
  10. 10.
    W. Metzner, D. Vollhardt, Phys. Rev. Lett. 62, 324 (1989)ADSCrossRefGoogle Scholar
  11. 11.
    A. Georges, G. Kotliar, W. Krauth, M.J. Rozenberg, Rev. Mod. Phys. 68, 13 (1996)ADSCrossRefGoogle Scholar
  12. 12.
    G. Kotliar, D. Vollhardt, Phys. Today 57, 53 (2004)CrossRefGoogle Scholar
  13. 13.
    D. Vollhardt, K. Byczuk, M. Kollar, in Strongly Correlated Systems, Springer Series in Solid-State Sciences, edited by A. Avella, F. Mancini, (Springer, Berlin Heidelberg, 2011), Springer Series in Solid-State Sciences, Vol. 171, p. 203Google Scholar
  14. 14.
    V.I. Anisimov, A.I. Poteryaev, M.A. Korotin, A.O. Anokhin, G. Kotliar, J. Phys.: Condens. Matter 9, 7359 (1997)ADSGoogle Scholar
  15. 15.
    A.I. Lichtenstein, M.I. Katsnelson, Phys. Rev. B 57, 6884 (1998)ADSCrossRefGoogle Scholar
  16. 16.
    A.I. Lichtenstein, M.I. Katsnelson, G. Kotliar, in Electron Correlations, Materials Properties, edited by A. Gonis, N. Kioussis, M. Ciftan (Kluwer Academic/Plenum, New York, 2002), p. 428Google Scholar
  17. 17.
    K. Held, I.A. Nekrasov, G. Keller, V. Eyert, N. Blümer, A.K. McMahan, R.T. Scalettar, T. Pruschke, V.I. Anisimov, D. Vollhardt, Phys. Status Solidi B 243, 2599 (2006)ADSCrossRefGoogle Scholar
  18. 18.
    G. Kotliar, S.Y. Savrasov, K. Haule, V.S. Oudovenko, O. Parcollet, C.A. Marianetti, Rev. Mod. Phys. 78, 865 (2006)ADSCrossRefGoogle Scholar
  19. 19.
    K. Held, Adv. Phys. 56, 829 (2007)ADSCrossRefGoogle Scholar
  20. 20.
    M.I. Katsnelson, V.Y. Irkhin, L. Chioncel, A.I. Lichtenstein, R.A. de Groot, Rev. Mod. Phys. 80, 315 (2008)ADSCrossRefGoogle Scholar
  21. 21.
    E. Pavarini, E. Koch, D. Vollhardt, A. Lichtenstein, The LDA+DMFT approach to strongly correlated materials, Modeling and Simulation, (Verlag des Forschungszentrum Jülich, 2011), Vol. 1 Google Scholar
  22. 22.
    K. Byczuk, J. Kunes, W. Hofstetter, D. Vollhardt, Phys. Rev. Lett. 108, 087004 (2012)ADSCrossRefGoogle Scholar
  23. 23.
    P. Thunström, I.D. Marco, O. Eriksson, Phys. Rev. Lett. 109, 186401 (2012)ADSCrossRefGoogle Scholar
  24. 24.
    I. Leonov, N. Binggeli, D. Korotin, V.I. Anisimov, N. Stojić, D. Vollhardt, Phys. Rev. Lett. 101, 096405 (2008)ADSCrossRefGoogle Scholar
  25. 25.
    I. Leonov, D. Korotin, N. Binggeli, V.I. Anisimov, D. Vollhardt, Phys. Rev. B 81, 075109 (2010)ADSCrossRefGoogle Scholar
  26. 26.
    J. Kunes, I. Leonov, M. Kollar, K. Byczuk, V.I. Anisimov, D. Vollhardt, Eur. Phys. J. Special Topics 180, 5 (2010)ADSCrossRefGoogle Scholar
  27. 27.
    I. Leonov, A.I. Poteryaev, V.I. Anisimov, D. Vollhardt, Phys. Rev. Lett. 106, 106405 (2011)ADSCrossRefGoogle Scholar
  28. 28.
    I. Leonov, A.I. Poteryaev, V.I. Anisimov, D. Vollhardt, Phys. Rev. B 85, R020401 (2012)ADSCrossRefGoogle Scholar
  29. 29.
    I. Leonov, V.I. Anisimov, D. Vollhardt, Phys. Rev. B 91, 195115 (2015)ADSCrossRefGoogle Scholar
  30. 30.
    R. Chitra, G. Kotliar, Phys. Rev. Lett. 83, 2386 (1999)ADSCrossRefGoogle Scholar
  31. 31.
    R. Zitzler, T. Pruschke, R. Bulla, Eur. Phys. J. B, 27, 473 (2002)ADSCrossRefGoogle Scholar
  32. 32.
    G. Sangiovanni, A. Toschi, E. Koch, K. Held, M. Capone, C. Castellani, O. Gunnarsson, S.K. Mo, J.W. Allen, H.D. Kim, A. Sekiyama, A. Yamasaki, S. Suga, P. Metcalf, Phys. Rev. B 73, 205121 (2006)ADSCrossRefGoogle Scholar
  33. 33.
    S. Hoshino, J. Otsuki, Y. Kuramoto, Phys. Rev. B 81, 113108 (2010)ADSCrossRefGoogle Scholar
  34. 34.
    J. Kuneš, D.M. Korotin, M.A. Korotin, V.I. Anisimov, P. Werner, Phys. Rev. Lett. 102, 146402 (2009)ADSCrossRefGoogle Scholar
  35. 35.
    J. Kuneš, V.Křápek, N. Parragh, G. Sangiovanni, A. Toschi, A.V. Kozhevnikov, Phys. Rev. Lett. 109, 117206 (2012)ADSCrossRefGoogle Scholar
  36. 36.
    E. Jakobi, S. Kanungo, S. Sarkar, S. Schmitt, T. Saha-Dasgupta, Phys. Rev. B 83, 041103 (2011)ADSCrossRefGoogle Scholar
  37. 37.
    M. Kim, B.I. Min, Phys. Rev. B 91, 205116 (2015)ADSCrossRefGoogle Scholar
  38. 38.
    H.T. Dang, J. Mravlje, A. Georges, A.J. Millis, Phys. Rev. B 91, 195149 (2015)ADSCrossRefGoogle Scholar
  39. 39.
    R. Arita, J. Kuneš, A.V. Kozhevnikov, A.G. Eguiluz, M. Imada, Phys. Rev. Lett. 108, 086403 (2012)ADSCrossRefGoogle Scholar
  40. 40.
    Z.P. Yin, K. Hual, G. Kotliar, Nat. Phys. 7, 294 (2011)CrossRefGoogle Scholar
  41. 41.
    M. Aichhorn, L. Pourovskii, A. Georges, Phys. Rev. B 84, 054529 (2011)ADSCrossRefGoogle Scholar
  42. 42.
    M.I. Katsnelson, A.I. Lichtenstein, J. Phys.: Condens. Matter 11, 1037 (1999)ADSGoogle Scholar
  43. 43.
    A.I. Lichtenstein, M.I. Katsnelson, G. Kotliar, Phys. Rev. Lett. 87, 067205 (2001)ADSCrossRefGoogle Scholar
  44. 44.
    M. Keller, W. Metzner, U. Schollwöck, Phys. Rev. Lett. 86, 4612 (2001)ADSCrossRefGoogle Scholar
  45. 45.
    M. Capone, C. Castellani, M. Grilli, Phys. Rev. Lett. 88, 126403 (2002)ADSCrossRefGoogle Scholar
  46. 46.
    M. Capone, M. Fabrizio, C. Castellani, E. Tosatti, Science 296, 2364 (2002)ADSCrossRefGoogle Scholar
  47. 47.
    A. Toschi, M. Capone, C. Castellani, Phys. Rev. B 72, 235118 (2005)ADSCrossRefGoogle Scholar
  48. 48.
    J. Bauer, A.C. Hewson, EPL 85, 27001 (2009)ADSCrossRefGoogle Scholar
  49. 49.
    J. Bauer, A.C. Hewson, N. Dupuis, Phys. Rev. B 79, 214518 (2009)ADSCrossRefGoogle Scholar
  50. 50.
    A. Koga, P. Werner, J. Phys. Soc. Jpn. 79, 064401 (2010)ADSCrossRefGoogle Scholar
  51. 51.
    A. Koga, P. Werner, Phys. Rev. B 91, 085108 (2015)ADSCrossRefGoogle Scholar
  52. 52.
    T.I. Vanhala, J.E. Baarsma, M.O.J. Heikkinen, M. Troyer, A. Harju, P. Törmä, Phys. Rev. B 91, 144510 (2015)ADSCrossRefGoogle Scholar
  53. 53.
    S. Hoshino, P. Werner, Phys. Rev. Lett. 115, 247001 (2015)ADSCrossRefGoogle Scholar
  54. 54.
    S. Hoshino, P. Werner, Phys. Rev. B 93, 155161 (2016)ADSCrossRefGoogle Scholar
  55. 55.
    T. Maier, M. Jarrell, T. Pruschke, J. Keller, Phys. Rev. Lett. 85, 1524 (2000)ADSCrossRefGoogle Scholar
  56. 56.
    T.A. Maier, M. Jarrell, T.C. Schulthess, P.R.C. Kent, J.B. White, Phys. Rev. Lett. 95, 237001 (2005)ADSCrossRefGoogle Scholar
  57. 57.
    K. Haule, G. Kotliar, Phys. Rev. B 76, 104509 (2007)ADSCrossRefGoogle Scholar
  58. 58.
    T. Maier, M. Jarrell, T. Pruschke, M.H. Hettler, Rev. Mod. Phys. 77, 1027 (2005)ADSCrossRefGoogle Scholar
  59. 59.
    J. Kuneš, Phys. Rev. B 83, 085102 (2011)ADSCrossRefGoogle Scholar
  60. 60.
    J. Kuneš, P. Augustinský, Phys. Rev. B 90, 235112 (2014)ADSCrossRefGoogle Scholar
  61. 61.
    J. Kuneš, Phys. Rev. B 90, 235140 (2014)ADSCrossRefGoogle Scholar
  62. 62.
    J. Kuneš, D. Geffroy, Phys. Rev. Lett. 116, 256403 (2016)ADSCrossRefGoogle Scholar
  63. 63.
    A. Sotnikov, J. Kuneš, Sci. Rep. 6, 30510 (2016)ADSCrossRefGoogle Scholar
  64. 64.
    T. Kaneko, Y. Ohta, Phys. Rev. B 90, 245144 (2014)ADSCrossRefGoogle Scholar
  65. 65.
    T. Kaneko, B. Zenker, H. Fehske, Y. Ohta, Phys. Rev. B 92, 115106 (2015)ADSCrossRefGoogle Scholar
  66. 66.
    S. Hoshino, J. Otsuki, Y. Kuramoto, Phys. Rev. Lett. 107, 247202 (2011)ADSCrossRefGoogle Scholar
  67. 67.
    P. Werner, S. Hoshino, H. Shinaoka, Phys. Rev. B 94, 245134 (2016)ADSCrossRefGoogle Scholar
  68. 68.
    P. Werner, A. Comanac, L. de’ Medici, M. Troyer, A.J. Millis, Phys. Rev. Lett. 97, 076405 (2006)ADSCrossRefGoogle Scholar
  69. 69.
    A. Albuquerque, F. Alet, P. Corboz, P. Dayal, A. Feiguin, S. Fuchs, L. Gamper, E. Gull, S.Gürtler, A. Honecker, R. Igarashi, M. Körner, A. Kozhevnikov, A. Läuchli, S. Manmana, M. Matsumoto, I. McCulloch, F. Michel, R. Noack, G. Pawłowski, L. Pollet, T. Pruschke, U. Schollwöck, S. Todo, S. Trebst, M. Troyer, P. Werner, S. Wessel, J. Magn. Magn. Mat. 310, 1187 (2007)ADSCrossRefGoogle Scholar
  70. 70.
    J.E. Gubernatis, M. Jarrell, R.N. Silver, D.S. Sivia, Phys. Rev. B 44, 6011 (1991)ADSCrossRefGoogle Scholar
  71. 71.
    J. Otsuki, M. Ohzeki, H. Shinaoka, K. Yoshimi, arXiv:1702.03056
  72. 72.
    C.A. Marianetti, K. Haule, G. Kotliar, M.J. Fluss, Phys. Rev. Lett. 101, 056403 (2008)ADSCrossRefGoogle Scholar
  73. 73.
    M. Jarrell, Phys. Rev. Lett. 69, 168 (1992)ADSCrossRefGoogle Scholar
  74. 74.
    J. Kuneš, V. Křápek, Phys. Rev. Lett. 106, 256401 (2011)ADSCrossRefGoogle Scholar
  75. 75.
    M. Jarrell, Phys. Rev. B 51, 7429 (1995)ADSCrossRefGoogle Scholar
  76. 76.
    M. Ulmke, V. Janiš, D. Vollhardt, Phys. Rev. B 51, 10411 (1995)ADSCrossRefGoogle Scholar
  77. 77.
    J. Kuneš, P. Augustinský, Phys. Rev. B 89, 115134 (2014)ADSCrossRefGoogle Scholar
  78. 78.
    L. Boehnke, A.I. Lichtenstein, M.I. Katsnelson, F. Lechermann, arXiv:1407.4795
  79. 79.
    K. Steiner, S. Hoshino, Y. Nomura, P. Werner, Phys. Rev. B 94, 075107 (2016)ADSCrossRefGoogle Scholar
  80. 80.
    L. Boehnke, F. Lechermann, Phys. Rev. B 85, 115128 (2012)ADSCrossRefGoogle Scholar
  81. 81.
    H. Park, K. Haule, G. Kotliar, Phys. Rev. Lett. 107, 137007 (2011)ADSCrossRefGoogle Scholar
  82. 82.
    Y. Tanabe, S. Sugano, J. Phys. Soc. Jpn. 9, 766 (1954)ADSCrossRefGoogle Scholar
  83. 83.
    J. Kuneš, A.V. Lukoyanov, V.I. Anisimov, R.T. Scalettar, W.E. Pickett, Nat. Mater. 7, 198 (2008)ADSCrossRefGoogle Scholar
  84. 84.
    A.O. Shorikov, Z.V. Pchelkina, V.I. Anisimov, S.L. Skornyakov, M.A. Korotin, Phys. Rev. B 82, 195101 (2010)ADSCrossRefGoogle Scholar
  85. 85.
    K. Ohta, R.E. Cohen, K. Hirose, K. Haule, K. Shimizu, Y. Ohishi, Phys. Rev. Lett. 108, 026403 (2012)ADSCrossRefGoogle Scholar
  86. 86.
    I. Leonov, Phys. Rev. B 92, 085142 (2015)ADSCrossRefGoogle Scholar
  87. 87.
    I. Leonov, L. Pourovskii, A. Georges, I.A. Abrikosov, Phys. Rev. B 94, 155135 (2016)ADSCrossRefGoogle Scholar
  88. 88.
    R.R. Heikes, R.C. Miller, R. Mazelsky, Physica 30, 1600 (1964)ADSCrossRefGoogle Scholar
  89. 89.
    C.S. Naiman, R. Gilmore, B. DiBartolo, A. Linz, R. Santoro, J. Appl. Phys. 36, 1044 (1965)ADSCrossRefGoogle Scholar
  90. 90.
    P.M. Raccah, J.B. Goodenough, Phys. Rev. 155, 932 (1967)ADSCrossRefGoogle Scholar
  91. 91.
    S. Yamaguchi, Y. Okimoto, H. Taniguchi, Y. Tokura, Phys. Rev. B 53, R2926 (1996)ADSCrossRefGoogle Scholar
  92. 92.
    C. Zobel, M. Kriener, D. Bruns, J. Baier, M. Grüninger, T. Lorenz, P. Reutler, A. Revcolevschi, Phys. Rev. B 66, 020402 (2002)ADSCrossRefGoogle Scholar
  93. 93.
    T. Kyômen, Y. Asaka, M. Itoh, Phys. Rev. B 67, 144424 (2003)ADSCrossRefGoogle Scholar
  94. 94.
    T. Kyômen, Y. Asaka, M. Itoh, Phys. Rev. B 71, 024418 (2005)ADSCrossRefGoogle Scholar
  95. 95.
    M. Abbate, J.C. Fuggle, A. Fujimori, L.H. Tjeng, C.T. Chen, R. Potze, G.A. Sawatzky, H. Eisaki, S. Uchida, Phys. Rev. B 47, 16124 (1993)ADSCrossRefGoogle Scholar
  96. 96.
    M.A. Korotin, S.Y. Ezhov, I.V. Solovyev, V.I. Anisimov, D.I. Khomskii, G.A. Sawatzky, Phys. Rev. B 54, 5309 (1996)ADSCrossRefGoogle Scholar
  97. 97.
    K. Knížek, P. Novák, Z. Jirák, Phys. Rev. B 71, 054420 (2005)ADSCrossRefGoogle Scholar
  98. 98.
    H. Hsu, K. Umemoto, M. Cococcioni, R. Wentzcovitch, Phys. Rev. B 79, 125124 (2009)ADSCrossRefGoogle Scholar
  99. 99.
    K. Knížek, Z. Jirák, J. Hejtmánek, P. Novák, W. Ku, Phys. Rev. B 79, 014430 (2009)ADSCrossRefGoogle Scholar
  100. 100.
    R. Eder, Phys. Rev. B 81, 035101 (2010)ADSCrossRefGoogle Scholar
  101. 101.
    V.Křápek, P. Novák, J. Kuneš, D. Novoselov, D.M. Korotin, V.I. Anisimov, Phys. Rev. B 86, 195104 (2012)ADSCrossRefGoogle Scholar
  102. 102.
    G. Zhang, E. Gorelov, E. Koch, E. Pavarini, Phys. Rev. B 86, 184413 (2012)ADSCrossRefGoogle Scholar
  103. 103.
    M. Karolak, M. Izquierdo, S.L. Molodtsov, A.I. Lichtenstein, Phys. Rev. Lett. 115, 046401 (2015)ADSCrossRefGoogle Scholar
  104. 104.
    T.C. Koethe, Ph.D. thesis, Universität zu Köln, 2006Google Scholar
  105. 105.
    M.W. Haverkort, Z. Hu, J.C. Cezar, T. Burnus, H. Hartmann, M. Reuther, C. Zobel, T. Lorenz, A. Tanaka, N.B. Brookes, H.H. Hsieh, H.J. Lin, C.T. Chen, L.H. Tjeng, Phys. Rev. Lett. 97, 176405 (2006)ADSCrossRefGoogle Scholar
  106. 106.
    J.F. Afonso, J. Kuneš, arXiv:1612.07576
  107. 107.
    P. Werner, A.J. Millis, Phys. Rev. Lett. 99, 126405 (2007)ADSCrossRefGoogle Scholar
  108. 108.
    R. Suzuki, T. Watanabe, S. Ishihara, Phys. Rev. B 80, 054410 (2009)ADSCrossRefGoogle Scholar
  109. 109.
    M. Blume, V.J. Emery, R.B. Griffiths, Phys. Rev. A 4, 1071 (1971)ADSCrossRefGoogle Scholar
  110. 110.
    W. Hoston, A.N. Berker, Phys. Rev. Lett. 67, 1027 (1991)ADSCrossRefGoogle Scholar
  111. 111.
    J. Kuneš, J. Phys.: Condens. Matter 27, 333201 (2015)ADSGoogle Scholar
  112. 112.
    B.I. Halperin, T.M. Rice, in Solid State Physics, edited by F. Seitz, D. Turnbull, H. Ehrenreich, (Academic Press, New York, 1968), Vol. 21, p. 115Google Scholar
  113. 113.
    B. Zocher, C. Timm, P.M.R. Brydon, Phys. Rev. B 84, 144425 (2011)ADSCrossRefGoogle Scholar
  114. 114.
    P.M.R. Brydon, C. Timm, Phys. Rev. B 79, 180504 (2009)ADSCrossRefGoogle Scholar
  115. 115.
    P.M.R. Brydon, C. Timm, Phys. Rev. B 80, 174401 (2009)ADSCrossRefGoogle Scholar
  116. 116.
    T. Kaneko, S. Ejima, H. Fehske, Y. Ohta, Phys. Rev. B 88, 035312 (2013)ADSCrossRefGoogle Scholar
  117. 117.
    G. Khaliullin, Phys. Rev. Lett. 111, 197201 (2013)ADSCrossRefGoogle Scholar
  118. 118.
    A. Jain, M. Krautloher, J. Porras, G.H. Ryu, D.P. Chen, D.L. Abernathy, J.T. Park, A. Ivanov, J. Chaloupka, G. Khaliullin, B. Keimer, B.J. Kim, arXiv:1510.07011
  119. 119.
    J. Chaloupka, G. Khaliullin, Phys. Rev. Lett. 116, 017203 (2016)ADSCrossRefGoogle Scholar
  120. 120.
    L. Boehnke, Susceptibilities in materials with multiple strongly correlated orbitals. Ph.D. thesis, University of Hamburg, 2015Google Scholar
  121. 121.
    J.P. Eisenstein, A.H. MacDonald, Nature 432, 691 (2004)ADSCrossRefGoogle Scholar
  122. 122.
    L.V. Pourovskii, B. Amadon, S. Biermann, A. Georges, Phys. Rev. B 76, 235101 (2007)ADSCrossRefGoogle Scholar
  123. 123.
    K. Haule, Phys. Rev. B 75, 155113 (2007)ADSCrossRefGoogle Scholar
  124. 124.
    B. Amadon, F. Lechermann, A. Georges, F. Jollet, T.O. Wehling, A.I. Lichtenstein, Phys. Rev. B 77, 205112 (2008)ADSCrossRefGoogle Scholar
  125. 125.
    M. Aichhorn, L. Pourovskii, V. Vildosola, M. Ferrero, O. Parcollet, T. Miyake, A. Georges, S. Biermann, Phys. Rev. B 80, 085101 (2009)ADSCrossRefGoogle Scholar
  126. 126.
    H. Park, A.J. Millis, C.A. Marianetti, Phys. Rev. B 90, 235103 (2014)ADSCrossRefGoogle Scholar
  127. 127.
    S.Y. Savrasov, G. Kotliar, E. Abrahams, Nature (London) 410, 793 (2001)ADSCrossRefGoogle Scholar
  128. 128.
    X. Dai, S.Y. Savrasov, G. Kotliar, A. Migliori, H. Ledbetter, E. Abrahams, Science 300, 953 (2003)ADSCrossRefGoogle Scholar
  129. 129.
    A.K. McMahan, K. Held, R.T. Scalettar, Phys. Rev. B 67, 075108 (2003)ADSCrossRefGoogle Scholar
  130. 130.
    B. Amadon, S. Biermann, A. Georges, F. Aryasetiawan, Phys. Rev. Lett. 96, 066402 (2006)ADSCrossRefGoogle Scholar
  131. 131.
    J. Bieder, B. Amadon, Phys. Rev. B 89, 195132 (2014)ADSCrossRefGoogle Scholar
  132. 132.
    A.A. Katanin, A.I. Poteryaev, A.V. Efremov, A.O. Shorikov, S.L. Skornyakov, M.A. Korotin, V.I. Anisimov, Phys. Rev. B 81, 045117 (2010)ADSCrossRefGoogle Scholar
  133. 133.
    A.S. Belozerov, I. Leonov, V.I. Anisimov, Phys. Rev. B 87, 125138 (2013)ADSCrossRefGoogle Scholar
  134. 134.
    I. Leonov, A.I. Poteryaev, Y.N. Gornostyrev, A.I. Lichtenstein, M.I. Katsnelson, V.I. Anisimov, D. Vollhardt, Sci. Rep. 4, 5585 (2014)ADSCrossRefGoogle Scholar
  135. 135.
    K. Glazyrin, L.V. Pourovskii, L. Dubrovinsky, O. Narygina, C. McCammon, B. Hewener, V. Schünemann, J. Wolny, K. Muffler, A.I. Chumakov, W. Crichton, M. Hanfland, V.B. Prakapenka, F. Tasnadi, M. Ekholm, M. Aichhorn, V. Vildosola, A.V. Ruban, M.I. Katsnelson, I.A. Abrikosov, Phys. Rev. Lett. 110, 117206 (2013)ADSCrossRefGoogle Scholar
  136. 136.
    L.V. Pourovskii, J. Mravlje, M. Ferrero, O. Parcollet, I.A. Abrikosov, Phys. Rev. B 90, 155120 (2014)ADSCrossRefGoogle Scholar
  137. 137.
    K. Held, G. Keller, V. Eyert, D. Vollhardt, V.I. Anisimov, Phys. Rev. Lett. 86, 5345 (2001)ADSCrossRefGoogle Scholar
  138. 138.
    G. Keller, K. Held, V. Eyert, D. Vollhardt, V.I. Anisimov, Phys. Rev. B 70, 205116 (2004)ADSCrossRefGoogle Scholar
  139. 139.
    S.K. Mo, J.D. Denlinger, H.D. Kim, J.H. Park, J.W. Allen, A. Sekiyama, A. Yamasaki, K. Kadono, S. Suga, Y. Saitoh, T. Muro, P. Metcalf, G. Keller, K. Held, V. Eyert, V.I. Anisimov, D. Vollhardt, Phys. Rev. Lett. 90, 186403 (2003)ADSCrossRefGoogle Scholar
  140. 140.
    S. Lupi, L. Baldassarre, B. Mansart, A. Perucchi, A. Barinov, P. Dudin, E. Papalazarou, F. Rodolakis, J.P. Rueff, J.P. Itié, S. Ravy, D. Nicoletti, P. Postorino, P. Hansmann, N. Parragh, A. Toschi, T. Saha-Dasgupta, O.K. Andersen, G. Sangiovanni, K. Held, M. Marsi, Nat. Commun. 1, 105 (2010)CrossRefGoogle Scholar
  141. 141.
    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
  142. 142.
    D. Grieger, C. Piefke, O.E. Peil, F. Lechermann, Phys. Rev. B 86, 155121 (2012)ADSCrossRefGoogle Scholar
  143. 143.
    D. Grieger, F. Lechermann, Phys. Rev. B 90, 115115 (2014)ADSCrossRefGoogle Scholar
  144. 144.
    I. Leonov, S. Skornyakov, V. Anisimov, D. Vollhardt, Phys. Rev. Lett. 115, 106402 (2015)ADSCrossRefGoogle Scholar
  145. 145.
    E. Pavarini, S. Biermann, A. Poteryaev, A.I. Lichtenstein, A. Georges, O.K. Andersen, Phys. Rev. Lett. 92, 176403 (2004)ADSCrossRefGoogle Scholar
  146. 146.
    S. Biermann, A. Poteryaev, A.I. Lichtenstein, A. Georges, Phys. Rev. Lett. 94, 026404 (2005)ADSCrossRefGoogle Scholar
  147. 147.
    A.I. Poteryaev, A.I. Lichtenstein, G. Kotliar, Phys. Rev. Lett. 93, 086401 (2004)ADSCrossRefGoogle Scholar
  148. 148.
    I. Leonov, V.I. Anisimov, D. Vollhardt, Phys. Rev. Lett. 112, 146401 (2014)ADSCrossRefGoogle Scholar
  149. 149.
    E. Pavarini, E. Koch, A.I. Lichtenstein, Phys. Rev. Lett. 101, 266405 (2008)ADSCrossRefGoogle Scholar
  150. 150.
    E. Pavarini, E. Koch, Phys. Rev. Lett. 104, 086402 (2010)ADSCrossRefGoogle Scholar
  151. 151.
    J. Kunes, V.I. Anisimov, Ann. Phys. (Berlin) 523, 682 (2011)ADSCrossRefGoogle Scholar
  152. 152.
    L. Huang, Y. Wang, X. Dai, Phys. Rev. B 85, 245110 (2012)ADSCrossRefGoogle Scholar
  153. 153.
    A.A. Dyachenko, A.O. Shorikov, A.V. Lukoyanov, V.I. Anisimov, JETP Lett. 96, 56 (2012)ADSCrossRefGoogle Scholar
  154. 154.
    X. Ren, I. Leonov, G. Keller, M. Kollar, I. Nekrasov, D. Vollhardt, Phys. Rev. B 74, 195114 (2006)ADSCrossRefGoogle Scholar
  155. 155.
    J. Kunes, V.I. Anisimov, A.V. Lukoyanov, D. Vollhardt, Phys. Rev. B 75, 165115 (2007)ADSCrossRefGoogle Scholar
  156. 156.
    J. Kunes, V.I. Anisimov, S.L. Skornyakov, A.V. Lukoyanov, D. Vollhardt, Phys. Rev. Lett. 99, 156404 (2007)ADSCrossRefGoogle Scholar
  157. 157.
    I.A. Nekrasov, N.S. Pavlov, M.V. Sadovskii, JETP Lett. 95, 581 (2012)ADSCrossRefGoogle Scholar
  158. 158.
    I.A. Nekrasov, N.S. Pavlov, M.V. Sadovskii, J. Exp. Theor. Phys. 116, 620 (2013)ADSCrossRefGoogle Scholar
  159. 159.
    P. Giannozzi, S. Baroni, N. Bonini, M. Calandra, R. Car, C. Cavazzoni, D. Ceresoli, G.L. Chiarotti, M. Cococcioni, I. Dabo, A.D. Corso, S. de Gironcoli, S. Fabris, G. Fratesi, R. Gebauer, U. Gerstmann, C. Gougoussis, A. Kokalj, M. Lazzeri, L. Martin-Samos, N. Marzari, F. Mauri, R. Mazzarello, S. Paolini, A. Pasquarello, L. Paulatto, C. Sbraccia, S. Scandolo, G. Sclauzero, A.P. Seitsonen, A. Smogunov, P. Umari, R.M. Wentzcovitch, J. Phys.: Condens. Matter 21, 395502 (2009)Google Scholar
  160. 160.
    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, A. Sekiyama, G. Keller, I. Leonov, X. Ren, D. Vollhardt, Phys. Rev. B 71, 125119 (2005)ADSCrossRefGoogle Scholar
  161. 161.
    G. Trimarchi, I. Leonov, N. Binggeli, D. Korotin, V.I. Anisimov, J. Phys.: Condens. Matter 20, 135227 (2008)ADSGoogle Scholar
  162. 162.
    N. Marzari, D. Vanderbilt, Phys. Rev. B 56, 12847 (1997)ADSCrossRefGoogle Scholar
  163. 163.
    D. Korotin, A.V. Kozhevnikov, S.L. Skornyakov, I. Leonov, N. Binggeli, V.I. Anisimov, G. Trimarchi, Eur. Phys. J. B 65, 91 (2008)ADSCrossRefGoogle Scholar
  164. 164.
    Z.S. Basinski, W. Hume-Rothery, A.L. Sutton, Proc. R. Soc. London Ser. A 229, 459 (1955)ADSCrossRefGoogle Scholar
  165. 165.
    R.W.G. Wyckoff (ed.), Crystal Structure (Wiley, New York, 1963), Vol. 1 Google Scholar
  166. 166.
    H. Hasegawa, D.G. Pettifor, Phys. Rev. Lett. 50, 130 (1983)ADSCrossRefGoogle Scholar
  167. 167.
    D.J. Singh, W.E. Pickett, H. Krakauer, Phys. Rev. B 43, 11628 (1991)ADSCrossRefGoogle Scholar
  168. 168.
    C. Amador, W.R.L. Lambrecht, B. Segall, Phys. Rev. B 46, 1870 (1992)ADSCrossRefGoogle Scholar
  169. 169.
    L. Stixrude, R.E. Cohen, D.J. Singh, Phys. Rev. B 50, 6442 (1994)ADSCrossRefGoogle Scholar
  170. 170.
    A.D. Corso, S. de Gironcoli, Phys. Rev. B 62, 273 (2000)ADSCrossRefGoogle Scholar
  171. 171.
    S.V. Okatov, A.R. Kuznetsov, Y.N. Gornostyrev, V.N. Urtsev, M.I. Katsnelson, Phys. Rev. B 79, 094111 (2009)ADSCrossRefGoogle Scholar
  172. 172.
    X. Sha, R.E. Cohen, Phys. Rev. B 73, 104303 (2006)ADSCrossRefGoogle Scholar
  173. 173.
    F.Körmann, A. Dick, B. Grabowski, T. Hickel, J. Neugebauer, Phys. Rev. B 85, 125104 (2012)ADSCrossRefGoogle Scholar
  174. 174.
    A.V. Ruban, V.I. Razumovskiy, Phys. Rev. B 85, 174407 (2012)ADSCrossRefGoogle Scholar
  175. 175.
    H.C. Hsueh, J. Crain, G.Y. Guo, H.Y. Chen, C.C. Lee, K.P. Chang, H.L. Shih, Phys. Rev. B 66, 052420 (2002)ADSCrossRefGoogle Scholar
  176. 176.
    J. Neuhaus, W. Petry, A. Krimmel, Physica B 234-236, 897 (1997)ADSCrossRefGoogle Scholar
  177. 177.
    J. Zarestky, C. Stassis, Phys. Rev. B 35, 4500 (1987)ADSCrossRefGoogle Scholar
  178. 178.
    W. Petry, J. Phys. IV 5, C2 (1995)Google Scholar
  179. 179.
    N.D. Drummond, G.J. Ackland, Phys. Rev. B 65, 184104 (2002)ADSCrossRefGoogle Scholar
  180. 180.
    Y. Kamihara, T. Watanabe, M. Hirano, H. Hosono, J. Am. Chem. Soc. 130, 3296 (2008)CrossRefGoogle Scholar
  181. 181.
    Z.A. Ren, W. Lu, J. Yang, W. Yi, X.L. Shen, Z.C. Li, G.C. Che, X.L. Dong, L.L. Sun, F. Zhou, Z.X. Zhao, Chin. Phys. Lett. 25, 2215 (2008)ADSCrossRefGoogle Scholar
  182. 182.
    X.H. Chen, T. Wu, G. Wu, R.H. Liu, H. Chen, D.F. Fang, Nature 453, 761 (2008)ADSCrossRefGoogle Scholar
  183. 183.
    J. Paglione, R.L. Greene, Nat. Phys. 6, 645 (2010)CrossRefGoogle Scholar
  184. 184.
    D.N. Basov, A.V. Chubukov, Nat. Phys. 7, 272 (2011)CrossRefGoogle Scholar
  185. 185.
    G.R. Stewart, Rev. Mod. Phys. 83, 1589 (2011)ADSCrossRefGoogle Scholar
  186. 186.
    P. Dai, J. Hu, E. Dagotto, Nat. Phys. 8, 709 (2012)CrossRefGoogle Scholar
  187. 187.
    F.C. Hsu, J.Y. Luo, K.W. Yeh, T.K. Chen, T.W. Huang, P.M. Wu, Y.C. Lee, Y.L. Huang, Y.Y. Chu, D.C. Yan, M.K. Wu, Proc. Natl. Acad. Sci. USA 105, 14262 (2008)ADSCrossRefGoogle Scholar
  188. 188.
    S. Margadonna, Y. Takabayashi, M.T. McDonald, K. Kasperkiewicz, Y. Mizuguchi, Y. Takano, A.N. Fitch, E. Suard, K. Prassides, Chem. Commun. p. 5607 (2008)Google Scholar
  189. 189.
    A.L.M.C. Lehman, K. Horigane, D. Louca, J. Phys.: Conf. Ser. 251, 012009 (2010)Google Scholar
  190. 190.
    Y. Mizuguchi, F. Tomioka, S. Tsuda, T. Yamaguchi, Y. Takano, Appl. Phys. Lett. 93, 152505 (2008)ADSCrossRefGoogle Scholar
  191. 191.
    S. Margadonna, Y. Takabayashi, Y. Ohishi, Y. Mizuguchi, Y. Takano, T. Kagayama, T. Nakagawa, M. Takata, K. Prassides, Phys. Rev. B 80, 064506 (2009)ADSCrossRefGoogle Scholar
  192. 192.
    S. Medvedev, T.M. McQueen, I.A. Troyan, T. Palasyuk, M.I. Eremets, R.J. Cava, S. Naghavi, F. Casper, V. Ksenofontov, G. Wortmann, C. Felser, Nature Mater. 8, 630 (2009)ADSCrossRefGoogle Scholar
  193. 193.
    B.C. Sales, A.S. Sefat, M.A. McGuire, R.Y. Jin, D. Mandrus, Y. Mozharivskyj, Phys. Rev. B 79, 094521 (2009)ADSCrossRefGoogle Scholar
  194. 194.
    A. Martinelli, A. Palenzona, M. Tropeano, C. Ferdeghini, M. Putti, M.R. Cimberle, T.D. Nguyen, M. Affronte, C. Ritter, Phys. Rev. B 81, 094115 (2010)ADSCrossRefGoogle Scholar
  195. 195.
    Y. Xia, D. Qian, L. Wray, D. Hsieh, G.F. Chen, J.L. Luo, N.L. Wang, M.Z. Hasan, Phys. Rev. Lett. 103, 037002 (2009)ADSCrossRefGoogle Scholar
  196. 196.
    A. Tamai, A.Y. Ganin, E. Rozbicki, J. Bacsa, W. Meevasana, P.D.C. King, M. Caffio, R. Schaub, S. Margadonna, K. Prassides, M.J. Rosseinsky, F. Baumberger, Phys. Rev. Lett. 104, 097002 (2010)ADSCrossRefGoogle Scholar
  197. 197.
    K. Okazaki, J. Phys.: Conf. Ser. 449, 012019 (2013)Google Scholar
  198. 198.
    J. Maletz, V.B. Zabolotnyy, D.V. Evtushinsky, S. Thirupathaiah, A.U.B. Wolter, L. Harnagea, A.N. Yaresko, A.N. Vasiliev, D.A. Chareev, A.E. Böhmer, F. Hardy, T. Wolf, C. Meingast, E.D.L. Rienks, B. Büchner, S.V. Borisenko, Phys. Rev. B 89, 220506 (2014)ADSCrossRefGoogle Scholar
  199. 199.
    B.C. Sales, A.S. Sefat, M.A. McGuire, R.Y. Jin, D. Mandrus, Y. Mozharivskyj, Phys. Rev. Lett. 105, 197001 (2010)CrossRefGoogle Scholar
  200. 200.
    F. Chen, B. Zhou, Y. Zhang, J. Wei, H.W. Ou, J.F. Zhao, C. He, Q.Q. Ge, M. Arita, K. Shimada, H. Namatame, M. Taniguchi, Z.Y. Lu, J. Hu, X.Y. Cui, D.L. Feng, Phys. Rev. B 81, 014526 (2010)ADSCrossRefGoogle Scholar
  201. 201.
    Y. Zhang, F. Chen, C. He, L.X. Yang, B.P. Xie, Y.L. Xie, X.H. Chen, M. Fang, M. Arita, K. Shimada, H. Namatame, M. Taniguchi, J.P. Hu, D.L. Feng, Phys. Rev. B 82, 165113 (2010)ADSCrossRefGoogle Scholar
  202. 202.
    J. Jiang, C. He, Y. Zhang, M. Xu, Q.Q. Ge, Z.R. Ye, F. Chen, B.P. Xie, D.L. Feng, Phys. Rev. B 88, 115130 (2013)ADSCrossRefGoogle Scholar
  203. 203.
    E. Ieki, K. Nakayama, Y. Miyata, T. Sato, H. Miao, N. Xu, X.P. Wang, P. Zhang, T. Qian, P. Richard, Z.J. Xu, J.S. Wen, G.D. Gu, H.Q. Luo, H.H. Wen, H. Ding, T. Takahashi, Phys. Rev. B 89, R140506 (2014)ADSCrossRefGoogle Scholar
  204. 204.
    K. Nakayama, Y. Miyata, G.N. Phan, T. Sato, Y. Tanabe, T. Urata, K. Tanigaki, T. Takahashi, Phys. Rev. Lett. 113, 237001 (2014)ADSCrossRefGoogle Scholar
  205. 205.
    I.I. Mazin, D.J. Singh, M.D. Johannes, M.H. Du, Phys. Rev. Lett. 101, 057003 (2008)ADSCrossRefGoogle Scholar
  206. 206.
    A.V. Chubukov, D.V. Efremov, I. Eremin, Phys. Rev. B 78, 134512 (2008)ADSCrossRefGoogle Scholar
  207. 207.
    A.D. Christianson, E.A. Goremychkin, R. Osborn, S. Rosenkranz, M.D. Lumsden, C.D. Malliakas, I.S. Todorov, H. Claus, D.Y. Chung, M.G. Kanatzidis, R.I. Bewley, T. Guidi, Nature 456, 930 (2008)ADSCrossRefGoogle Scholar
  208. 208.
    M.D. Lumsden, A.D. Christianson, D. Parshall, M.B. Stone, S.E. Nagler, G.J. MacDougall, H.A. Mook, K. Lokshin, T. Egami, D.L. Abernathy, E.A. Goremychkin, R. Osborn, M.A. McGuire, A.S. Sefat, R. Jin, B.C. Sales, D. Mandrus, Phys. Rev. Lett. 102, 107005 (2009)ADSCrossRefGoogle Scholar
  209. 209.
    Y. Qiu, W. Bao, Y. Zhao, C. Broholm, V. Stanev, Z. Tesanovic, Y.C. Gasparovic, S. Chang, J. Hu, B. Qian, M. Fang, Z. Mao, Phys. Rev. Lett. 103, 067008 (2009)ADSCrossRefGoogle Scholar
  210. 210.
    M.D. Lumsden, A.D. Christianson, E.A. Goremychkin, S.E. Nagler, H.A. Mook, M.B. Stone, D.L. Abernathy, T. Guidi, G.J. MacDougall, C. de la Cruz, A.S. Sefat, M.A. McGuire, B.C. Sales, D. Mandrus, Nat. Phys. 6, 182 (2010)CrossRefGoogle Scholar
  211. 211.
    W. Bao, Y. Qiu, Q. Huang, M.A. Green, P. Zajdel, M.R. Fitzsimmons, M. Zhernenkov, S. Chang, M. Fang, B. Qian, E.K. Vehstedt, J. Yang, H.M. Pham, L. Spinu, Z.Q. Mao, Phys. Rev. Lett. 102, 247001 (2009)ADSCrossRefGoogle Scholar
  212. 212.
    T.J. Liu, J. Hu, B. Qian, D. Fobes, Z.Q. Mao, W. Bao, M. Reehuis, S.A.J. Kimber, K. Prokeš, S. Matas, D.N. Argyriou, A. Hiess, A. Rotaru, H. Pham, L. Spinu, Y. Qiu, V. Thampy, A.T. Savici, J.A. Rodriguez, C. Broholm, Nature Mater. 9, 718 (2010)ADSCrossRefGoogle Scholar
  213. 213.
    O.J. Lipscombe, G.F. Chen, C. Fang, T.G. Perring, D.L. Abernathy, A.D. Christianson, T. Egami, N. Wang, J. Hu, P. Dai, Phys. Rev. Lett. 106, 057004 (2011)ADSCrossRefGoogle Scholar
  214. 214.
    S. Li, C. de la Cruz, Q. Huang, Y. Chen, J.W. Lynn, J. Hu, Y.L. Huang, F.C. Hsu, K.W. Yeh, M.K. Wu, P. Dai, Phys. Rev. B 79, 054503 (2009)ADSCrossRefGoogle Scholar
  215. 215.
    C. Zhang, W. Yi, L. Sun, X.J. Chen, R.J. Hemley, H.k. Mao, W. Lu, X. Dong, L. Bai, J. Liu, A.F. Moreira Dos Santos, J.J. Molaison, C.A. Tulk, G. Chen, N. Wang, Z. Zhao, Phys. Rev. B 80, 144519 (2009)ADSCrossRefGoogle Scholar
  216. 216.
    S.L. Skornyakov, V.I. Anisimov, D. Vollhardt, I. Leonov. (unpublished)Google Scholar
  217. 217.
    E. Gull, A.J. Millis, A.I. Lichtenstein, A.N. Rubtsov, M. Troyer, P. Werner, Rev. Mod. Phys. 83, 349 (2011)ADSCrossRefGoogle Scholar
  218. 218.
    K. Haule, J.H. Shim, G. Kotliar, Phys. Rev. Lett. 100, 226402 (2008)ADSCrossRefGoogle Scholar
  219. 219.
    V.I. Anisimov, D.M. Korotin, M.A. Korotin, A.V. Kozhevnikov, J. Kuneš, A.O. Shorikov, S.L. Skornyakov, S.V. Streltsov, J. Phys.: Condens. Matter 21, 075602 (2009)ADSGoogle Scholar
  220. 220.
    S.L. Skornyakov, A.V. Efremov, N.A. Skorikov, M.A. Korotin, Y.A. Izyumov, V.I. Anisimov, A.V. Kozhevnikov, D. Vollhardt, Phys. Rev. B 80, 092501 (2009)ADSCrossRefGoogle Scholar
  221. 221.
    S.L. Skornyakov, A.A. Katanin, V.I. Anisimov, Phys. Rev. Lett. 106, 047007 (2011)ADSCrossRefGoogle Scholar
  222. 222.
    Z.P. Yin, K. Haule, G. Kotliar, Nature Mater. 10, 932 (2011)ADSCrossRefGoogle Scholar
  223. 223.
    J.M. Tomczak, M. van Schilfgaarde, G. Kotliar, Phys. Rev. Lett. 109, 237010 (2012)ADSCrossRefGoogle Scholar
  224. 224.
    Z.P. Yin, K. Haule, G. Kotliar, Phys. Rev. B 86, 195141 (2012)ADSCrossRefGoogle Scholar
  225. 225.
    A. Georges, L. de Medici, J. Mravlje, Ann. Rev. Cond. Mat. Phys. 4, 137 (2013)ADSCrossRefGoogle Scholar
  226. 226.
    C. Zhang, L.W. Harriger, Z. Yin, W. Lv, M. Wang, G. Tan, Y. Song, D.L. Abernathy, W. Tian, T. Egami, K. Haule, G. Kotliar, P. Dai, Phys. Rev. Lett. 112, 217202 (2014)ADSCrossRefGoogle Scholar
  227. 227.
    S. Mandal, R.E. Cohen, K. Haule, Phys. Rev. B 89, R220502 (2014)ADSCrossRefGoogle Scholar
  228. 228.
    K. Haule, T. Birol, Phys. Rev. Lett. 115, 256402 (2015)ADSCrossRefGoogle Scholar
  229. 229.
    K. Haule, G.L. Pascut, Phys. Rev. B 94, 195146 (2016)ADSCrossRefGoogle Scholar
  230. 230.
    V. Galitskii, A. Migdal, Sov. Phys. JETP 7, 96 (1958)Google Scholar
  231. 231.
    A.D. Corso, Ph.D. thesis, SISSA, Trieste (1993)Google Scholar
  232. 232.
    A.D. Corso, A. Pasquarello, A. Baldereschi, Phys. Rev. B 56, R11369 (1997)ADSCrossRefGoogle Scholar
  233. 233.
    D. Alfè, Comp. Phys. Comm. 180, 2622 (2009)ADSCrossRefGoogle Scholar
  234. 234.
    H. Aoki, N. Tsuji, M. Eckstein, M. Kollar, T. Oka, P. Werner, Rev. Mod. Phys. 86, 779 (2014)ADSCrossRefGoogle Scholar
  235. 235.
    B. Bauer, L.D. Carr, H.G. Evertz, A. Feiguin, J. Freire, S. Fuchs, L. Gamper, J. Gukelberger, E. Gull, S. Guertler, A. Hehn, R. Igarashi, S.V. Isakov, D. Koop, P.N. Ma, P. Mates, H. Matsuo, O. Parcollet, G. Pawłowski, J.D. Picon, L. Pollet, E. Santos, V.W. Scarola, U. Schollwck, C. Silva, B. Surer, S. Todo, S. Trebst, M. Troyer, M.L. Wall, P. Werner, S. Wessel, J. Stat. Mech.: Theory Exp. 2011, P05001 (2011)Google Scholar
  236. 236.
    P. Seth, I. Krivenko, M. Ferrero, O. Parcollet, Comp. Phys. Comm. 200, 274 (2016)ADSCrossRefGoogle Scholar
  237. 237.
    N. Parragh, A. Toschi, K. Held, G. Sangiovanni, Phys. Rev. B 86, 155158 (2012)ADSCrossRefGoogle Scholar
  238. 238.
    Y. Lu, M. Höppner, O. Gunnarsson, M.W. Haverkort, Phys. Rev. B 90, 085102 (2014)ADSCrossRefGoogle Scholar
  239. 239.
    F.A. Wolf, A. Go, I.P. McCulloch, A.J. Millis, U. Schollwöck, Phys. Rev. X 5, 041032 (2015)Google Scholar
  240. 240.
    H. Hafermann, K.R. Patton, P. Werner, Phys. Rev. B 85, 205106 (2012)ADSCrossRefGoogle Scholar
  241. 241.
    L. Boehnke, H. Hafermann, M. Ferrero, F. Lechermann, O. Parcollet, Phys. Rev. B 84, 075145 (2011)ADSCrossRefGoogle Scholar
  242. 242.
    P. Gunacker, M. Wallerberger, E. Gull, A. Hausoel, G. Sangiovanni, K. Held, Phys. Rev. B 92, 155102 (2015)ADSCrossRefGoogle Scholar
  243. 243.
    P. Gunacker, M. Wallerberger, T. Ribic, A. Hausoel, G. Sangiovanni, K. Held, Phys. Rev. B 94, 125153 (2016)ADSCrossRefGoogle Scholar
  244. 244.
    A. Toschi, A.A. Katanin, K. Held, Phys. Rev. B 75, 045118 (2007)ADSCrossRefGoogle Scholar
  245. 245.
    A.N. Rubtsov, M.I. Katsnelson, A.I. Lichtenstein, Phys. Rev. B 77, 033101 (2008)ADSCrossRefGoogle Scholar
  246. 246.
    A.N. Rubtsov, M.I. Katsnelson, A.I. Lichtenstein, Annals of Physics 327, 1320 (2012)ADSCrossRefGoogle Scholar
  247. 247.
    E.G.C.P. van Loon, F. Krien, H. Hafermann, E.A. Stepanov, A.I. Lichtenstein, M.I. Katsnelson, Phys. Rev. B 93, 155162 (2016)ADSCrossRefGoogle Scholar

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Authors and Affiliations

  1. 1.Institute of Solid State Physics, TU WienWienAustria
  2. 2.Institute of Physics, Czech Academy of SciencesPraha 8Czech Republic
  3. 3.Theoretical Physics III, Center for Electronic Correlations and Magnetism, Institute of Physics, University of AugsburgAugsburgGermany
  4. 4.Central European Institute of Technology, Brno University of TechnologyBrnoCzech Republic

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