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The European Physical Journal Special Topics

, Volume 226, Issue 11, pp 2565–2590 | Cite as

Merging GW with DMFT and non-local correlations beyond

  • J. M. Tomczak
  • P. Liu
  • A. Toschi
  • G. Kresse
  • K. Held
Open Access
Review
Part of the following topical collections:
  1. Dynamical Mean-Field Approach with Predictive Power for Strongly Correlated Materials

Abstract

We review recent developments in electronic structure calculations that go beyond state-of-the-art methods such as density functional theory (DFT) and dynamical mean field theory (DMFT). Specifically, we discuss the following methods: GW as implemented in the Vienna ab initio simulation package (VASP) with the self energy on the imaginary frequency axis, GW+DMFT, and ab initio dynamical vertex approximation (DΓA). The latter includes the physics of GW, DMFT and non-local correlations beyond, and allows for calculating (quantum) critical exponents. We present results obtained by the three methods with a focus on the benchmark material SrVO3.

References

  1. 1.
    W. Kohn, L. Sham, Phys. Rev. 140, A1133 (1965)ADSCrossRefGoogle Scholar
  2. 2.
    P. Hohenberg, W. Kohn, Phys. Rev. 136, B864 (1964)ADSCrossRefGoogle Scholar
  3. 3.
    R. Jones, O. Gunnarsson, Rev. Mod. Phys. 61, 689 (1989)ADSCrossRefGoogle Scholar
  4. 4.
    R.M. Martin, Electronic Structure: Basic Theory and Practical Methods (Cambridge University Press, Cambridge, 2004)Google Scholar
  5. 5.
    R.M. Martin, L. Reining, D.M. Ceperley, Interacting Electrons: Theory and Computational Approaches (Cambridge University Press, Cambridge, 2016)Google Scholar
  6. 6.
    A. Seidl, A. Görling, P. Vogl, J.A. Majewski, M. Levy, Phys. Rev. B 53, 3764 (1996)ADSCrossRefGoogle Scholar
  7. 7.
    C. Adamo, V. Barone, J. Chem. Phys. 110, 6158 (1999)ADSCrossRefGoogle Scholar
  8. 8.
    J. Heyd, G.E. Scuseria, M. Ernzerhof, J. Chem. Phys. 118, 8207 (2003)ADSCrossRefGoogle Scholar
  9. 9.
    F. Fuchs, J. Furthmüller, F. Bechstedt, M. Shishkin, G. Kresse, Phys. Rev. B 76, 115109 (2007)ADSCrossRefGoogle Scholar
  10. 10.
    C. Freysoldt, B. Grabowski, T. Hickel, J. Neugebauer, G. Kresse, A. Janotti, C.G. Van de Walle, Rev. Mod. Phys. 86, 253 (2014)ADSCrossRefGoogle Scholar
  11. 11.
    L. Hedin, Phys. Rev. 139, A796 (1965)ADSCrossRefGoogle Scholar
  12. 12.
    S.V. Faleev, M. van Schilfgaarde, T. Kotani, Phys. Rev. Lett. 93, 126406 (2004)ADSCrossRefGoogle Scholar
  13. 13.
    A.N. Chantis, M. van Schilfgaarde, T. Kotani, Phys. Rev. Lett. 96, 086405 (2006)ADSCrossRefGoogle Scholar
  14. 14.
    M. Shishkin, G. Kresse, Phys. Rev. B 74, 035101 (2006)ADSCrossRefGoogle Scholar
  15. 15.
    P. Liu, M. Kaltak, J.c.v. Klimeš, G. Kresse, Phys. Rev. B 94, 165109 (2016)ADSCrossRefGoogle Scholar
  16. 16.
    A. Galler, P. Thunström, P. Gunacker, J.M. Tomczak, K. Held, Phys. Rev. B 95, 115107 (2017)ADSCrossRefGoogle Scholar
  17. 17.
    R.W. Godby, M. Schlüter, L.J. Sham, Phys. Rev. B 37, 10159 (1988)ADSCrossRefGoogle Scholar
  18. 18.
    F. Aryasetiawan, O. Gunnarsson, Rep. Prog. Phys. 61, 237 (1998)ADSCrossRefGoogle Scholar
  19. 19.
    A.L. Kutepov, Phys. Rev. B 94, 155101 (2016)ADSCrossRefGoogle Scholar
  20. 20.
    H. Cao, Z. Yu, P. Lu, L.W. Wang, Phys. Rev. B 95, 035139 (2017)ADSCrossRefGoogle Scholar
  21. 21.
    M. Imada, A. Fujimori, Y. Tokura, Rev. Mod. Phys. 70, 1039 (1998)ADSCrossRefGoogle Scholar
  22. 22.
    W. Metzner, D. Vollhardt, Phys. Rev. Lett. 62, 324 (1989)ADSCrossRefGoogle Scholar
  23. 23.
    A. Georges, G. Kotliar, Phys. Rev. B 45, 6479 (1992)ADSCrossRefGoogle Scholar
  24. 24.
    A. Georges, G. Kotliar, W. Krauth, M.J. Rozenberg, Rev. Mod. Phys. 68, 13 (1996)ADSCrossRefGoogle Scholar
  25. 25.
    A.I. Lichtenstein, M.I. Katsnelson, Phys. Rev. B 57, 6884 (1998)ADSCrossRefGoogle Scholar
  26. 26.
    V.I. Anisimov, A.I. Poteryaev, M.A. Korotin, A.O. Anokhin, G. Kotliar, J. Phys.: Condens. Matter 9, 7359 (1997)ADSGoogle Scholar
  27. 27.
    G. Kotliar, S.Y. Savrasov, K. Haule, V.S. Oudovenko, O. Parcollet, C.A. Marianetti, Rev. Mod. Phys. 78, 865 (2006)ADSCrossRefGoogle Scholar
  28. 28.
    K. Held, Adv. Phys. 56, 829 (2007)ADSCrossRefGoogle Scholar
  29. 29.
    I.A. Nekrasov, K. Held, G. Keller, D.E. Kondakov, T. Pruschke, M. Kollar, O.K. Andersen, V.I. Anisimov, D. Vollhardt, Phys. Rev. B 73, 155112 (2006)ADSCrossRefGoogle Scholar
  30. 30.
    K. Byczuk, M. Kollar, K. Held, Y.F. Yang, I.A. Nekrasov, T. Pruschke, D. Vollhardt, Nat. Phys. 3, 168 (2007)CrossRefGoogle Scholar
  31. 31.
    A. Toschi, M. Capone, C. Castellani, K. Held, Phys. Rev. Lett 102, 076402 (2009)ADSCrossRefGoogle Scholar
  32. 32.
    K. Held, R. Peters, A. Toschi, Phys. Rev. Lett. 110, 246402 (2013)ADSCrossRefGoogle Scholar
  33. 33.
    G. Keller, K. Held, V. Eyert, D. Vollhardt, V.I. Anisimov, Phys. Rev. B 70, 205116 (2004)ADSCrossRefGoogle Scholar
  34. 34.
    K. Held, G. Keller, V. Eyert, D. Vollhardt, V.I. Anisimov, Phys. Rev. Lett. 86, 5345 (2001)ADSCrossRefGoogle Scholar
  35. 35.
    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
  36. 36.
    P. Hansmann, A. Toschi, G. Sangiovanni, T. Saha-Dasgupta, S. Lupi, M. Maresi, K. Held, Phys. Status Solidi B 250, 1251 (2013)ADSCrossRefGoogle Scholar
  37. 37.
    K. Held, A.K. McMahan, R.T. Scalettar, Phys. Rev. Lett. 87, 276404 (2001)ADSCrossRefGoogle Scholar
  38. 38.
    A.K. McMahan, K. Held, R.T. Scalettar, Phys. Rev. B 67, 075108 (2003)ADSCrossRefGoogle Scholar
  39. 39.
    S. Okamoto, A.J. Millis, Phys. Rev. B 72, 235108 (2005)ADSCrossRefGoogle Scholar
  40. 40.
    P. Hansmann, X. Yang, A. Toschi, G. Khaliullin, O.K. Andersen, K. Held, Phys. Rev. Lett. 103, 016401 (2009)ADSCrossRefGoogle Scholar
  41. 41.
    Z. Zhong, M. Wallerberger, J.M. Tomczak, C. Taranto, N. Parragh, A. Toschi, G. Sangiovanni, K. Held, Phys. Rev. Lett. 114, 246401 (2015)ADSCrossRefGoogle Scholar
  42. 42.
    G. Lantz, M. Hajlaoui, E. Papalazarou, V.L.R. Jacques, A. Mazzotti, M. Marsi, S. Lupi, M. Amati, L. Gregoratti, L. Si, Z. Zhong, K. Held, Phys. Rev. Lett. 115, 236802 (2015)ADSCrossRefGoogle Scholar
  43. 43.
    A. Valli, H. Das, G. Sangiovanni, T. Saha-Dasgupta, K. Held, Phys. Rev. B 92, 115143 (2015)ADSCrossRefGoogle Scholar
  44. 44.
    S. Backes, T.C. Rödel, F. Fortuna, E. Frantzeskakis, P. Le Fèvre, F. Bertran, M. Kobayashi, R. Yukawa, T. Mitsuhashi, M. Kitamura, K. Horiba, H. Kumigashira, R. Saint-Martin, A. Fouchet, B. Berini, Y. Dumont, A.J. Kim, F. Lechermann, H.O. Jeschke, M.J. Rozenberg, R. Valentí, A.F. Santander-Syro, Phys. Rev. B 94, 241110 (2016)ADSCrossRefGoogle Scholar
  45. 45.
    V.I. Anisimov, J. Zaanen, O.K. Andersen, Phys. Rev. B 44, 943 (1991)ADSCrossRefGoogle Scholar
  46. 46.
    P. Hansmann, N. Parragh, A. Toschi, G. Sangiovanni, K. Held, New J. Phys. 16, 033009 (2014)ADSCrossRefGoogle Scholar
  47. 47.
    H.T. Dang, A.J. Millis, C.A. Marianetti, Phys. Rev. B 89, 161113 (2014)ADSCrossRefGoogle Scholar
  48. 48.
    K. Haule, T. Birol, G. Kotliar, Phys. Rev. B 90, 075136 (2014)ADSCrossRefGoogle Scholar
  49. 49.
    P. Sun, G. Kotliar, Phys. Rev. B 66, 085120 (2002)ADSCrossRefGoogle Scholar
  50. 50.
    S. Biermann, F. Aryasetiawan, A. Georges, Phys. Rev. Lett. 90, 086402 (2003)ADSCrossRefGoogle Scholar
  51. 51.
    J.M. Tomczak, M. Casula, T. Miyake, F. Aryasetiawan, S. Biermann, EPL 100, 67001 (2012)ADSCrossRefGoogle Scholar
  52. 52.
    J.M. Tomczak, M. Casula, T. Miyake, S. Biermann, Phys. Rev. B 90, 165138 (2014)ADSCrossRefGoogle Scholar
  53. 53.
    K. Held, C. Taranto, G. Rohringer, A. Toschi, Lecture Notes of the Autumn School 2011 Hands-on LDA+DMFT, Forschungszentrum Juelich GmbH (publisher) [arXiv:1109.3972] (2011)
  54. 54.
    F. Aryasetiawan, S. Biermann, A. Georges, Proceedings of the conference “Coincidence Studies of Surfaces, Thin Films and Nanostructures”, Ringberg castle, Sept. 2003 (2004)Google Scholar
  55. 55.
    S. Biermann, J. Phys.: Condens. Matter 26, 173202 (2014)Google Scholar
  56. 56.
    P. Werner, M. Casula, J. Phys.: Condens. Matter 28, 383001 (2016)ADSGoogle Scholar
  57. 57.
    M.H. Hettler, A.N. Tahvildar-Zadeh, M. Jarrell, T. Pruschke, H.R. Krshnamurthy, Phys. Rev. B 58, R7475 (1998)ADSCrossRefGoogle Scholar
  58. 58.
    A.I. Lichtenstein, M.I. Katsnelson, Phys. Rev. B 62, R9283 (2000)ADSCrossRefGoogle Scholar
  59. 59.
    G. Kotliar, S. Savrasov, G. Palsson, G. Biroli, Phys. Rev. Lett. 87, 186401 (2001)ADSCrossRefGoogle Scholar
  60. 60.
    A. Toschi, A.A. Katanin, K. Held, Phys. Rev. B 75, 045118 (2007)ADSCrossRefGoogle Scholar
  61. 61.
    H. Kusunose, J. Phys. Soc. Jpn 75, 054713 (2006)ADSCrossRefGoogle Scholar
  62. 62.
    A.N. Rubtsov, M.I. Katsnelson, A.I. Lichtenstein, Phys. Rev. B 77, 033101 (2008)ADSCrossRefGoogle Scholar
  63. 63.
    G. Rohringer, A. Toschi, H. Hafermann, K. Held, V.I. Anisimov, A.A. Katanin, Phys. Rev. B 88, 115112 (2013)ADSCrossRefGoogle Scholar
  64. 64.
    C. Taranto, S. Andergassen, J. Bauer, K. Held, A. Katanin, W. Metzner, G. Rohringer, A. Toschi, Phys. Rev. Lett. 112, 196402 (2014)ADSCrossRefGoogle Scholar
  65. 65.
    T. Ayral, O. Parcollet, Phys Rev. B 92, 115109 (2015)ADSCrossRefGoogle Scholar
  66. 66.
    G. Li, Phys. Rev. B 91, 165134 (2015)ADSCrossRefGoogle Scholar
  67. 67.
    T. Maier, M. Jarrell, T. Pruschke, M.H. Hettler, Rev. Mod. Phys. 77, 1027 (2005)ADSCrossRefGoogle Scholar
  68. 68.
    G. Rohringer, A. Toschi, A. Katanin, K. Held, Phys. Rev. Lett. 107, 256402 (2011)ADSCrossRefGoogle Scholar
  69. 69.
    D. Hirschmeier, H. Hafermann, E. Gull, A.I. Lichtenstein, A.E. Antipov, Phys. Rev. B 92, 144409 (2015)ADSCrossRefGoogle Scholar
  70. 70.
    A.E. Antipov, E. Gull, S. Kirchner, Phys. Rev. Lett. 112, 226401 (2014)ADSCrossRefGoogle Scholar
  71. 71.
    T. Schäfer, A.A. Katanin, K. Held, A. Toschi, arXiv:1605.06355 (2016)
  72. 72.
    T. Schäfer, F. Geles, D. Rost, G. Rohringer, E. Arrigoni, K. Held, N. Blümer, M. Aichhorn, A. Toschi, Phys. Rev. B 91, 125109 (2015)ADSCrossRefGoogle Scholar
  73. 73.
    A.A. Katanin, A. Toschi, K. Held, Phys. Rev. B 80, 075104 (2009)ADSCrossRefGoogle Scholar
  74. 74.
    A. Toschi, G. Rohringer, A. Katanin, K. Held, Ann. Phys. 523, 698 (2011)CrossRefGoogle Scholar
  75. 75.
    K. Held, Lecture Notes “Autumn School on Correlated Electrons. DMFT at 25: Infinite Dimensions”, Reihe Modeling and Simulation, Vol. 4, Forschungszentrum Juelich GmbH (publisher) [arXiv:1411.5191] (2014)
  76. 76.
    G. Rohringer, New routes towards a theoretical treatment of nonlocal electronic correlations, Ph.D. thesis, Vienna University of Technology, 2013Google Scholar
  77. 77.
    G. Strinati, H.J. Mattausch, W. Hanke, Phys. Rev. Lett. 45, 290 (1980)ADSCrossRefGoogle Scholar
  78. 78.
    M.S. Hybertsen, S.G. Louie, Phys. Rev. B 34, 5390 (1986)ADSCrossRefGoogle Scholar
  79. 79.
    F. Bechstedt, F. Fuchs, G. Kresse, Phys. Stat. Sol. B 246, 1877 (2009)ADSCrossRefGoogle Scholar
  80. 80.
    M. Shishkin, M. Marsman, G. Kresse, Phys. Rev. Lett. 99, 246403 (2007)ADSCrossRefGoogle Scholar
  81. 81.
    M.C. Payne, M.P. Teter, D.C. Allan, T.A. Arias, J.D. Joannopoulos, Rev. Mod. Phys. 64, 1045 (1992)ADSCrossRefGoogle Scholar
  82. 82.
    H.N. Rojas, R.W. Godby, R.J. Needs, Phys. Rev. Lett. 74, 1827 (1995)ADSCrossRefGoogle Scholar
  83. 83.
    L. Steinbeck, A. Rubio, L. Reining, M. Torrent, I. White, W. Godby, Comput. Phys. Commun. 125, 105 (2000)ADSCrossRefGoogle Scholar
  84. 84.
    M. Kaltak, J. Klimeš, G. Kresse, J. Chem. Theory Comput. 10, 2498 (2014)CrossRefGoogle Scholar
  85. 85.
    A. Grüneis, G. Kresse, Y. Hinuma, F. Oba, Phys. Rev. Lett. 112, 096401 (2014)ADSCrossRefGoogle Scholar
  86. 86.
    M. Kaltak, J. Klimeš, G. Kresse, Phys. Rev. B 90, 054115 (2014)ADSCrossRefGoogle Scholar
  87. 87.
    F. Aryasetiawan, M. Imada, A. Georges, G. Kotliar, S. Biermann, A.I. Lichtenstein, Phys. Rev. B 70, 195104 (2004)ADSCrossRefGoogle Scholar
  88. 88.
    J. Klimeš, M. Kaltak, G. Kresse, Phys. Rev. B 90, 075125 (2014)ADSCrossRefGoogle Scholar
  89. 89.
    B.C. Shih, Y. Xue, P. Zhang, M.L. Cohen, S.G. Louie, Phys. Rev. Lett. 105, 146401 (2010)ADSCrossRefGoogle Scholar
  90. 90.
    C. Friedrich, M.C. Müller, S. Blügel, Phys. Rev. B 83, 081101 (2011) [Erratum: Phys. Rev. B 84, 039906(E) (2011)]ADSCrossRefGoogle Scholar
  91. 91.
    E. Maggio, P. Liu, M.J. van Setten, G. Kresse, J. Chem. Theory Comput. 13, 635 (2017)CrossRefGoogle Scholar
  92. 92.
    H.J. Vidberg, J.W. Serene, J. Low Temp. Phys. 29, 179 (1977)ADSCrossRefGoogle Scholar
  93. 93.
    F. Aryasetiawan, K. Karlsson, O. Jepsen, U. Schönberger, Phys. Rev. B 74, 125106 (2006)ADSCrossRefGoogle Scholar
  94. 94.
    L. Vaugier, H. Jiang, S. Biermann, Phys. Rev. B 86, 165105 (2012)ADSCrossRefGoogle Scholar
  95. 95.
    L. Boehnke, F. Nilsson, F. Aryasetiawan, P. Werner, Phys. Rev. B 94, 201106 (2016)ADSCrossRefGoogle Scholar
  96. 96.
    M. Guzzo, G. Lani, F. Sottile, P. Romaniello, M. Gatti, J.J. Kas, J.J. Rehr, M.G. Silly, F. Sirotti, L. Reining, Phys. Rev. Lett. 107, 166401 (2011)ADSCrossRefGoogle Scholar
  97. 97.
    V.I. Anisimov, O. Gunnarsson, Phys. Rev. B 43, 7570 (1991)ADSCrossRefGoogle Scholar
  98. 98.
    T. Miyake, F. Aryasetiawan, Phys. Rev. B 77, 085122 (2008)ADSCrossRefGoogle Scholar
  99. 99.
    J.M. Tomczak, T. Miyake, F. Aryasetiawan, Phys. Rev. B 81, 115116 (2010)ADSCrossRefGoogle Scholar
  100. 100.
    B. Amadon, F. Lechermann, A. Georges, F. Jollet, T.O. Wehling, A.I. Lichtenstein, Phys. Rev. B 77, 205112 (2008)ADSCrossRefGoogle Scholar
  101. 101.
    M. Karolak, T.O. Wehling, F. Lechermann, A.I. Lichtenstein, J. Phys.: Condens. Matter 23, 085601 (2011)ADSGoogle Scholar
  102. 102.
    S.K. Panda, B. Pal, S. Mandal, M. Gorgoi, S. Das, I. Sarkar, W. Drube, W. Sun, I. Di Marco, A. Lindblad, P. Thunström, A. Delin, O. Karis, Y.O. Kvashnin, M. van Schilfgaarde, O. Eriksson, D.D. Sarma, Phys. Rev. B 93, 235138 (2016)ADSCrossRefGoogle Scholar
  103. 103.
    J.M. Tomczak, S. Biermann, EPL 86, 37004 (2009)ADSCrossRefGoogle Scholar
  104. 104.
    J.M. Tomczak, L.V. Pourovskii, L. Vaugier, A. Georges, S. Biermann, Proc. Natl. Acad. Sci. USA 110, 904 (2013)ADSCrossRefGoogle Scholar
  105. 105.
    R. Sakuma, C. Martins, T. Miyake, F. Aryasetiawan, Phys. Rev. B 89, 235119 (2014)ADSCrossRefGoogle Scholar
  106. 106.
    J.M. Tomczak, K. Haule, T. Miyake, A. Georges, G. Kotliar, Phys. Rev. B 82, 085104 (2010)ADSCrossRefGoogle Scholar
  107. 107.
    J.M. Tomczak, M. van Schilfgaarde, G. Kotliar, Phys. Rev. Lett. 109, 237010 (2012)ADSCrossRefGoogle Scholar
  108. 108.
    A. van Roekeghem, T. Ayral, J.M. Tomczak, M. Casula, N. Xu, H. Ding, M. Ferrero, O. Parcollet, H. Jiang, S. Biermann, Phys. Rev. Lett. 113, 266403 (2014)ADSCrossRefGoogle Scholar
  109. 109.
    M. Casula, A. Rubtsov, S. Biermann, Phys. Rev. B 85, 035115 (2012)ADSCrossRefGoogle Scholar
  110. 110.
    L. Huang, Y. Wang, EPL 99, 67003 (2012)ADSCrossRefGoogle Scholar
  111. 111.
    P. Werner, M. Casula, T. Miyake, F. Aryasetiawan, A.J. Millis, S. Biermann, Nat. Phys. 8, 331 (2012)CrossRefGoogle Scholar
  112. 112.
    P. Werner, R. Sakuma, F. Nilsson, F. Aryasetiawan, Phys. Rev. B 91, 125142 (2015)ADSCrossRefGoogle Scholar
  113. 113.
    T. Ayral, P. Werner, S. Biermann, Phys. Rev. Lett. 109, 226401 (2012)ADSCrossRefGoogle Scholar
  114. 114.
    T. Ayral, S. Biermann, P. Werner, Phys. Rev. B 87, 125149 (2013)ADSCrossRefGoogle Scholar
  115. 115.
    H. Park, K. Haule, G. Kotliar, Phys. Rev. Lett. 107, 137007 (2011)ADSCrossRefGoogle Scholar
  116. 116.
    A. Toschi, R. Arita, P. Hansmann, G. Sangiovanni, K. Held, Phys. Rev. B 86, 064411 (2012)ADSCrossRefGoogle Scholar
  117. 117.
    A. Galler, C. Taranto, M. Wallerberger, M. Kaltak, G. Kresse, G. Sangiovanni, A. Toschi, K. Held, Phys. Rev. B 92, 205132 (2015)ADSCrossRefGoogle Scholar
  118. 118.
    A.M. Sengupta, A. Georges, Phys. Rev. B 52, 10295 (1995)ADSCrossRefGoogle Scholar
  119. 119.
    Q. Si, J.L. Smith, Phys. Rev. Lett. 77, 3391 (1996)ADSCrossRefGoogle Scholar
  120. 120.
    P. Werner, A.J. Millis, Phys. Rev. Lett. 104, 146401 (2010)ADSCrossRefGoogle Scholar
  121. 121.
    K. Steiner, Y. Nomura, P. Werner, Phys. Rev. B 92, 115123 (2015)ADSCrossRefGoogle Scholar
  122. 122.
    Y. Nomura, M. Kaltak, K. Nakamura, C. Taranto, S. Sakai, A. Toschi, R. Arita, K. Held, G. Kresse, M. Imada, Phys. Rev. B 86, 085117 (2012)ADSCrossRefGoogle Scholar
  123. 123.
    P. Hansmann, T. Ayral, L. Vaugier, P. Werner, S. Biermann, Phys. Rev. Lett. 110, 166401 (2013)ADSCrossRefGoogle Scholar
  124. 124.
    C. Taranto, M. Kaltak, N. Parragh, G. Sangiovanni, G. Kresse, A. Toschi, K. Held, Phys. Rev. B 88, 165119 (2013)ADSCrossRefGoogle Scholar
  125. 125.
    R. Sakuma, P. Werner, F. Aryasetiawan, Phys. Rev. B 88, 235110 (2013)ADSCrossRefGoogle Scholar
  126. 126.
    M. Casula, P. Werner, L. Vaugier, F. Aryasetiawan, T. Miyake, A.J. Millis, S. Biermann, Phys. Rev. Lett. 109, 126408 (2012)ADSCrossRefGoogle Scholar
  127. 127.
    E. Pavarini, S. Biermann, A. Poteryaev, A.I. Lichtenstein, A. Georges, O.K. Andersen, Phys. Rev. Lett. 92, 176403 (2004)ADSCrossRefGoogle Scholar
  128. 128.
    A. Sekiyama, H. Fujiwara, S. Imada, S. Suga, H. Eisaki, S.I. Uchida, K. Takegahara, H. Harima, Y. Saitoh, I.A. Nekrasov, G. Keller, D.E. Kondakov, A.V. Kozhevnikov, T. Pruschke, K. Held, D. Vollhardt, V.I. Anisimov, Phys. Rev. Lett. 93, 156402 (2004)ADSCrossRefGoogle Scholar
  129. 129.
    T. Miyake, C. Martins, R. Sakuma, F. Aryasetiawan, Phys. Rev. B 87, 115110 (2013)ADSCrossRefGoogle Scholar
  130. 130.
    A. van Roekeghem, S. Biermann, EPL 108, 57003 (2014)ADSCrossRefGoogle Scholar
  131. 131.
    N. Parragh, A. Toschi, K. Held, G. Sangiovanni, Phys. Rev. B 86, 155158 (2012)ADSCrossRefGoogle Scholar
  132. 132.
    M. Wallerberger, PhD Thesis, TU Wien, 2016Google Scholar
  133. 133.
    K. Nakamura, Y. Nohara, Y. Yosimoto, Y. Nomura, Phys. Rev. B 93, 085124 (2016)ADSCrossRefGoogle Scholar
  134. 134.
    S. Aizaki, T. Yoshida, K. Yoshimatsu, M. Takizawa, M. Minohara, S. Ideta, A. Fujimori, K. Gupta, P. Mahadevan, K. Horiba, H. Kumigashira, M. Oshima, Phys. Rev. Lett. 109, 056401 (2012)ADSCrossRefGoogle Scholar
  135. 135.
    M. Takizawa, M. Minohara, H. Kumigashira, D. Toyota, M. Oshima, H. Wadati, T. Yoshida, A. Fujimori, M. Lippmaa, M. Kawasaki, H. Koinuma, G. Sordi, M. Rozenberg, Phys. Rev. B 80, 235104 (2009)ADSCrossRefGoogle Scholar
  136. 136.
    J.M. Tomczak, J. Phys.: Conf. Ser. 592, 012055 (2015)Google Scholar
  137. 137.
    S. Choi, A. Kutepov, K. Haule, M. van Schilfgaarde, G. Kotliar, Npj Quantum Mater. 1, 16001 (2016)CrossRefGoogle Scholar
  138. 138.
    L. Sponza, P. Pisanti, A. Vishina, D. Pashov, C. Weber, M. van Schilfgaarde, S. Acharya, J. Vidal, G. Kotliar, Phys. Rev. B 95, 041112 (2017)ADSCrossRefGoogle Scholar
  139. 139.
    A.L. Kutepov, J. Phys.: Condens. Matter 27, 315603 (2015)ADSMathSciNetGoogle Scholar
  140. 140.
    J. Lee, K. Haule, arXiv:1611.07090 (2016)
  141. 141.
    C.O. Almbladh, U.V. Barth, R.V. Leeuwen, Int. J. Mod. Phys. B 13, 535 (1999)ADSCrossRefGoogle Scholar
  142. 142.
    H. Hafermann, E.G.C.P. van Loon, M.I. Katsnelson, A.I. Lichtenstein, O. Parcollet, Phys. Rev. B 90, 235105 (2014)ADSCrossRefGoogle Scholar
  143. 143.
    G. Rohringer, A. Valli, A. Toschi, Phys. Rev. B 86, 125114 (2012)ADSCrossRefGoogle Scholar
  144. 144.
    A. Valli, T. Schäfer, P. Thunström, G. Rohringer, S. Andergassen, G. Sangiovanni, K. Held, A. Toschi, Phys. Rev. B 91, 115115 (2015)ADSCrossRefGoogle Scholar
  145. 145.
    G. Li, N. Wentzell, P. Pudleiner, P. Thunström, K. Held, Phys. Rev. B 93, 165103 (2016)ADSCrossRefGoogle Scholar
  146. 146.
    E. Gull, A.J. Millis, A.I. Lichtenstein, A.N. Rubtsov, M. Troyer, P. Werner, Rev. Mod. Phys. 83, 349 (2011)ADSCrossRefGoogle Scholar
  147. 147.
    P. Gunacker, M. Wallerberger, E. Gull, A. Hausoel, G. Sangiovanni, K. Held, Phys. Rev. B 92, 155102 (2015)ADSCrossRefGoogle Scholar
  148. 148.
    H. Hafermann, Phys. Rev. B 89, 235128 (2014)ADSCrossRefGoogle Scholar
  149. 149.
    P. Gunacker, M. Wallerberger, T. Ribic, A. Hausoel, G. Sangiovanni, K. Held, Phys. Rev. B 94, 125153 (2016)ADSCrossRefGoogle Scholar
  150. 150.
    J. Kuneš, Phys. Rev. B 83, 085102 (2011)ADSCrossRefGoogle Scholar
  151. 151.
    N. Wentzell, G. Li, A. Tagliavini, C. Taranto, G. Rohringer, K. Held, A. Toschi, S. Andergassen, arXiv:1610.06520 (2016)
  152. 152.
    T. Schäfer, A. Toschi, K. Held, J. Magn. Magn. Mater. 400, 107 (2016)ADSCrossRefGoogle Scholar
  153. 153.
    G. Rohringer, A. Toschi, Phys. Rev. B 94, 125144 (2016)ADSCrossRefGoogle Scholar
  154. 154.
    J. Otsuki, H. Hafermann, A.I. Lichtenstein, Phys. Rev. B 90, 235132 (2014)ADSCrossRefGoogle Scholar
  155. 155.
    A.N. Rubtsov, M.I. Katsnelson, A.I. Lichtenstein, Ann. Phys. 327(5), 1320 (2012)ADSCrossRefGoogle Scholar
  156. 156.
    O. Gunnarsson, T. Schäfer, J.P.F. LeBlanc, E. Gull, J. Merino, G. Sangiovanni, G. Rohringer, A. Toschi, Phys. Rev. Lett. 114, 236402 (2015)ADSCrossRefGoogle Scholar
  157. 157.
    A.N. Tahvildar-Zadeh, J.K. Freericks, M. Jarrell, Phys. Rev. B 55, 942 (1997)ADSCrossRefGoogle Scholar
  158. 158.
    J.A. Hertz, Phys. Rev. B 14, 1165 (1976)ADSCrossRefGoogle Scholar
  159. 159.
    A.J. Millis, Phys. Rev. B 48, 7183 (1993)ADSCrossRefGoogle Scholar
  160. 160.
    T. Schäfer, S. Ciuchi, M. Wallerberger, P. Thunström, O. Gunnarsson, G. Sangiovanni, G. Rohringer, A. Toschi, Phys. Rev. B 94, 235108 (2016)ADSCrossRefGoogle Scholar
  161. 161.
    T. Schäfer, A. Toschi, J.M. Tomczak, Phys. Rev. B 91, 121107 (2015)ADSCrossRefGoogle Scholar
  162. 162.
    P. Pudleiner, T. Schäfer, D. Rost, G. Li, K. Held, N. Blümer, Phys. Rev. B 93, 195134 (2016)ADSCrossRefGoogle Scholar

Copyright information

© The Author(s) 2017

Open Access This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Authors and Affiliations

  • J. M. Tomczak
    • 1
  • P. Liu
    • 2
    • 3
  • A. Toschi
    • 1
  • G. Kresse
    • 2
  • K. Held
    • 1
  1. 1.Institute of Solid State Physics, TU WienWienAustria
  2. 2.University of Vienna, Faculty of Physics and Center for Computational Materials ScienceViennaAustria
  3. 3.Shenyang National Laboratory for Materials Science, Institute of Metal Research, University of Chinese Academy of SciencesP.R.China

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