RSS feeds
РусскийEnglish
Issue 5, 2024
Volume year page
Issues Authors PACS Subscription For authors

Issues

 / 

2023

 / 

August

←  →

Reviews of topical problems


Mean-field concept and post-DMFT methods in the modern theory of correlated systems

†  a, b, ‡  a, c, §  a, c
a International Center for Quantum Optics and Quantum Technologies (the Russian Quantum Center), ul. Novaya 100, Skolkovo, Moscow Region, 143025, Russian Federation
b National Research Nuclear University ‘MEPhI’, Kashirskoe shosse 31, Moscow, 115409, Russian Federation
c Lomonosov Moscow State University, Vorobevy Gory, Moscow, 119991, Russian Federation

We briefly review methods for modeling correlated systems. The concept of correlations is of fundamental physical importance for systems such as Mott—Hubbard insulators, high-temperature superconductors, molecular magnets, and twisted bilayer graphene. With the Hubbard model chosen as a reference, we systematically describe various numerical methods, starting with the mean-field and related theories that map the physical system under study onto an effective interaction-free ensemble. We also discuss the dynamical mean-field theory (DMFT), which is one of the most common modern methods to describe local correlations exactly. DMFT-based diagram methods incorporate effects of nonlocal physics to varying degrees, with the local correlations taken into account in full. In addition, we describe the nondiagram fluctuating local field method, whereby fluctuations of the leading collective modes of the system can be treated nonperturbatively.

Fulltext pdf (1015 KB)
Fulltext is also available at DOI: 10.3367/UFNe.2022.09.039231
Keywords: strongly correlated systems, dynamical mean-field theory, fluctuations
PACS: 71.10.−w
DOI: 10.3367/UFNe.2022.09.039231
URL: https://ufn.ru/en/articles/2023/8/b/
001112646900002
2-s2.0-85163322735
2023PhyU...66..775L
Citation: Lyakhova Ya S, Astretsov G V, Rubtsov A N "Mean-field concept and post-DMFT methods in the modern theory of correlated systems" Phys. Usp. 66 775–793 (2023)
BibTexBibNote ® (generic)BibNote ® (RIS)MedlineRefWorks

Received: 14th, March 2022, revised: 6th, September 2022, 7th, September 2022

Оригинал: Ляхова Я С, Астрецов Г В, Рубцов А Н «Концепция среднего поля и методы пост-DMFT в современной теории коррелированных систем» УФН 193 825–844 (2023); DOI: 10.3367/UFNr.2022.09.039231

References (186) ↓ Similar articles (20)

  1. Mott N F Proc. Phys. Soc. A 62 416 (1949)
  2. Roth L M J. Phys. Chem. Solids 23 433 (1962)
  3. Hubbard J Proc. R. Soc. Lond. A 276 238 (1963)
  4. Hubbard J Proc. R. Soc. Lond. A 277 237 (1964)
  5. Hubbard J Proc. R. Soc. Lond. A 281 401 (1964)
  6. Izyumov Yu A Phys. Usp. 38 385 (1995); Izyumov Yu A Usp. Fiz. Nauk 165 403 (1995)
  7. van Loon E G C P, Katsnelson M I J. Phys. Conf. Ser. 1136 012006 (2018)
  8. Bünemann J et al J. Phys. Condens. Matter 19 326217 (2007)
  9. Aryasetiawan F et al Phys. Rev. B 70 195104 (2004)
  10. Bednorz J G, Müller K A Z. Phys. B 64 189 (1986)
  11. Bardeen J, Cooper L N, Schrieffer J R Phys. Rev. 108 1175 (1957)
  12. Damascelli A, Hussain Z, Shen Z-X Rev. Mod. Phys. 75 473 (2003)
  13. Reznik D et al Nature 440 1170 (2006)
  14. Lanzara A et al Nature 412 510 (2001)
  15. Mackenzie A P, Maeno Y Rev. Mod. Phys. 75 657 (2003)
  16. Kamihara Y et al J. Am. Chem. Soc. 130 3296 (2008)
  17. Petrovic C et al J. Phys. Condens. Matter 13 L337 (2001)
  18. Stewart S R Rev. Mod. Phys. 56 755 (1984)
  19. Lee P A, Nagaosa N, Wen X-G Rev. Mod. Phys. 78 17 (2006)
  20. Yan S, Huse D A, White S R Science 332 1173 (2011)
  21. Norman M R Rev. Mod. Phys. 88 041002 (2016)
  22. Izyumov Yu A, Kurmaev E Z Phys. Usp. 51 23 (2008); Izyumov Yu A, Kurmaev E Z Usp. Fiz. Nauk 178 25 (2008)
  23. Bakr W S et al Nature 462 74 (2009)
  24. Mazurenko A et al Nature 545 462 (2017)
  25. Geim A K, Grigorieva I V Nature 499 419 (2013)
  26. Yankowitz M et al Science 363 1059 (2019)
  27. Balents L et al Nat. Phys. 16 725 (2020)
  28. Kennes D M et al Nat. Phys. 17 155 (2021)
  29. Christos M, Sachdev S, Scheurer M S Phys. Rev. X 12 021018 (2022)
  30. Song Z-D, Bernevig B A Phys. Rev. Lett. 129 047601 (2022)
  31. Weinberg P, Bukov M SciPost Phys. 2 003 (2017)
  32. Weinberg P, Bukov M SciPost Phys. 7 020 (2019)
  33. Liu X-Y, Qi C Comput. Phys. Commun. 259 107349 (2021)
  34. Amaricci A et al Comput. Phys. Commun. 273 108261 (2022)
  35. Yoshimi K, Tsumuraya T, Misawa T Phys. Rev. Res. 3 043224 (2021)
  36. Ochi M, Koshino M, Kuroki K Phys. Rev. B 98 081102 (2018)
  37. Repellin C et al Phys. Rev. Lett. 124 187601 (2020)
  38. Xie F et al Phys. Rev. B 103 205416 (2021)
  39. Potasz P, Xie M, MacDonald A H Phys. Rev. Lett. 127 147203 (2021)
  40. Austin B M, Zubarev D Y, Lester W A (Jr.) Chem. Rev. 112 263 (2012)
  41. Needs R J et al J. Chem. Phys. 152 154106 (2020)
  42. Foulkes W M C et al Rev. Mod. Phys. 73 33 (2001)
  43. Burovski E A et al Phys. Rev. Lett. 87 186402 (2001)
  44. Wagner L K, Ceperley D M Rep. Prog. Phys. 79 094501 (2016)
  45. Nakano K et al Phys. Rev. B 103 L121110 (2021)
  46. Becca F, Sorella S Quantum Monte Carlo Approaches For Correlated Systems (Cambridge: Cambridge Univ. Press, 2017)
  47. Li Z-X, Yao H Annu. Rev. Condens. Matter Phys. 10 337 (2019)
  48. Hangleiter D et al Sci. Adv. 6 eabb8341 (2020)
  49. Huggins W J et al Nature 603 416 (2022)
  50. Huang E W et al Npj Quantum Mater. 3 22 (2018)
  51. Jiang H-C, Devereaux T P Science 365 1424 (2019)
  52. Bollmark G, Laflorencie N, Kantian A Phys. Rev. B 102 195145 (2020)
  53. Bollmark G et al Phys. Rev. X 13 011039 (2023)
  54. Schollwöck U Rev. Mod. Phys. 77 259 (2005)
  55. Schollwöck U Ann. Physics 326 (1) 96 (2011)
  56. Baiardi A, Reiher M J. Chem. Phys. 152 040903 (2020)
  57. Jiang Y-F et al Phys. Rev. Res. 2 033073 (2020)
  58. Peng C et al New J. Phys. 23 123004 (2021)
  59. Mai P et al Proc. Natl. Acad. Sci. USA 119 e2112806119 (2022)
  60. Stemmle C, Paulus B, Legeza Ö Phys. Rev. A 97 022505 (2018)
  61. Beran P et al J. Chem. Theory Comput. 17 7575 (2021)
  62. Sugihara T J. High Energy Phys. 2004 007 (2004)
  63. Stoudenmire E M, White S R Annu. Rev. Condens. Matter Phys. 3 111 (2012)
  64. Li Q et al Phys. Rev. Lett. 130 226502 (2023)
  65. Tazhigulov R N et al PRX Quantum 3 040318 (2022)
  66. Stair N H, Evangelista F A PRX Quantum 2 030301 (2021)
  67. Bravyi S B, Kitaev A Yu Ann. Physics 298 210 (2002)
  68. Seeley J T, Richard M J, Love P J J. Chem. Phys. 137 224109 (2012)
  69. Tranter A et al J. Chem. Theory Comput. 14 5617 (2018)
  70. Gutzwiller M C Phys. Rev. Lett. 10 159 (1963)
  71. Predescu C Phys. Rev. E 66 066133 (2002)
  72. Feynman R P Statistical Mechanics (Reading, MA: W.A. Benjamin, 1972)
  73. Stoner E C Proc. R. Soc. Lond. A 165 372 (1938)
  74. Becke A D J. Chem. Phys. 140 18A301 (2014)
  75. Jones R O Rev. Mod. Phys. 87 897 (2015)
  76. Hasnip P J et al Philos. Trans. R. Soc. A 372 20130270 (2014)
  77. Zhang T et al RSC Adv. 5 106877 (2015)
  78. Hohenberg P, Kohn W Phys. Rev. 136 B864 (1964)
  79. Hybertsen M S, Schlüter M, Christensen N E Phys. Rev. B 39 9028 (1989)
  80. McMahan A K, Annett J F, Martin R M Phys. Rev. B 42 6268 (1990)
  81. Gunnarsson O, Schönhammer K Phys. Rev. Lett. 56 1968 (1986)
  82. Abrikosov A A, Gorkov L P, Dzyaloshinski I E Methods Of Quantum Field Theory In Statistical Physics (New York: Dover Publ., 1975); Translated from Russian, Abrikosov A A, Gorkov L P, Dzyaloshinski I E Metody Kvantovoi Teorii Polya V Statisticheskoi Fizike (Moscow: Ripol Klassik, 2013)
  83. Mahan G D Many-Particle Physics (Berlin: Springer, 2013)
  84. Coleman P Introduction To Many-Body Physics (New York: Cambridge Univ. Press, 2015)
  85. Nelson W et al Phys. Rev. A 75 032505 (2007)
  86. Romaniello P, Guyot S, Reining L J. Chem. Phys. 131 154111 (2009)
  87. Schmidt P S, Patrick C E, Thygesen K S Phys. Rev. B 96 205206 (2017)
  88. Pavlyukh Y, Stefanucci G, van Leeuwen R Phys. Rev. B 102 045121 (2020)
  89. van Schilfgaarde M, Kotani T, Faleev S Phys. Rev. Lett. 96 226402 (2006)
  90. Anisimov V I, Aryasetiawan F, Lichtenstein A J. Phys. Condens. Matter 9 767 (1997)
  91. Metzner W, Vollhardt D Phys. Rev. Lett. 62 324 (1989)
  92. Yonezawa F, Morigaki K Prog. Theor. Phys. Suppl. 53 1 (1973)
  93. Altland A, Simons B D Condensed Matter Field Theory (Cambridge: Cambridge Univ. Press, 2010)
  94. Anderson P W Phys. Rev. 109 1492 (1958)
  95. Elliott R J, Krumhansl J A, Leath P L Rev. Mod. Phys. 46 465 (1974)
  96. Rubtsov A N, Savkin V V, Lichtenstein A I Phys. Rev. B 72 035122 (2005)
  97. Werner P, Millis A J Phys. Rev. B 74 155107 (2006)
  98. Gull E et al Rev. Mod. Phys. 83 349 (2011)
  99. Zingl M et al Physica B 536 254 (2018)
  100. de Souza Melo B M et al J. Phys. Condens. Matter 32 095602 (2020)
  101. Loh E Y (Jr.) et al Phys. Rev. B 41 9301 (1990)
  102. Cohen G et al Phys. Rev. Lett. 115 266802 (2015)
  103. Jarrell M, Gubernatis J E Phys. Rep. 269 133 (1996)
  104. Vidberg H J, Serene J W J. Low Temp. Phys. 29 179 (1977)
  105. Logan D E, Galpin M R J. Phys. Condens. Matter 28 025601 (2016)
  106. Park H, Haule K, Kotliar G Phys. Rev. Lett. 101 186403 (2008)
  107. Sun P, Kotliar G Phys. Rev. B 66 085120 (2002)
  108. Biermann S, Aryasetiawan F, Georges A Phys. Rev. Lett. 90 086402 (2003)
  109. Ayral T, Biermann S, Werner P Phys. Rev. B 87 125149 (2013)
  110. Kotliar G et al Rev. Mod. Phys. 78 865 (2006)
  111. Georges A et al Rev. Mod. Phys. 68 13 (1996)
  112. Held K et al Phys. Rev. Lett. 86 5345 (2001)
  113. McWhan D B, Rice T M, Remeika J P Phys. Rev. Lett. 23 1384 (1969)
  114. Zang J et al Phys. Rev. X 12 021064 (2022)
  115. Maier T et al Rev. Mod. Phys. 77 1027 (2005)
  116. Kotliar G et al Phys. Rev. Lett. 87 186401 (2001)
  117. LeBlanc J P F et al Phys. Rev. X 5 041041 (2015)
  118. Stanescu T D et al Ann. Physics 321 1682 (2006)
  119. Chen Y-H et al Phys. Rev. B 91 045122 (2015)
  120. Zhang Y Z, Imada M Phys. Rev. B 76 045108 (2007)
  121. Kyung B, Tremblay A-M S Phys. Rev. Lett. 97 046402 (2006)
  122. Lichtenstein A I, Katsnelson M I Phys. Rev. B 62 R9283 (2000)
  123. Hettler M H et al Phys. Rev. B 58 R7475 (1998)
  124. Maier T A et al Phys. Rev. Lett. 95 237001 (2005)
  125. Gull E, Parcollet O, Millis A J Phys. Rev. Lett. 110 216405 (2013)
  126. Aryanpour K, Maier Th A, Jarrell M Phys. Rev. B 71 037101 (2005)
  127. Potthoff M, Aichhorn M, Dahnken C Phys. Rev. Lett. 91 206402 (2003)
  128. Dahnken C et al Phys. Rev. B 70 245110 (2004)
  129. Aichhorn M et al Phys. Rev. B 74 235117 (2006)
  130. Sénéchal D et al Phys. Rev. Lett. 94 156404 (2005)
  131. Rohringer G et al Rev. Mod. Phys. 90 025003 (2018)
  132. Stratonovich R L Sov. Phys. Dokl. 2 416 (1957); Stratonovich R L Dokl. Akad. Nauk SSSR 115 1097 (1957)
  133. Hubbard J Phys. Rev. Lett. 3 77 (1959)
  134. Rubtsov A N, Katsnelson M I, Lichtenstein A I Phys. Rev. B 77 033101 (2008)
  135. Rubtsov A N et al Phys. Rev. B 79 045133 (2009)
  136. Rubtsov A N, Katsnelson M I, Lichtenstein A I Ann. Physics 327 1320 (2012)
  137. Jaeckel J, Wetterich C Phys. Rev. D 68 025020 (2003)
  138. Baier T, Bick E, Wetterich C Phys. Rev. B 70 125111 (2004)
  139. Toschi A, Katanin A A, Held K Phys. Rev. B 75 045118 (2007)
  140. Maier T A, Jarrell M S, Scalapino D J Phys. Rev. Lett. 96 047005 (2006)
  141. Ribic T et al Phys. Rev. B 96 235127 (2017)
  142. Sadovskii M V et al Phys. Rev. B 72 155105 (2005)
  143. Kuchinskii E Z, Nekrasov I A, Sadovskii M V Phys. Usp. 55 325 (2012); Kuchinskii E Z, Nekrasov I A, Sadovskii M V Usp. Fiz. Nauk 182 345 (2012)
  144. Kitatani M, Tsuji N, Aoki H Phys. Rev. B 92 085104 (2015)
  145. Ayral T, Parcollet O Phys. Rev. B 92 115109 (2015)
  146. Ayral T, Parcollet O Phys. Rev. B 93 235124 (2016)
  147. Vučičević J, Ayral T, Parcollet O Phys. Rev. B 96 104504 (2017)
  148. Cao X et al Phys. Rev. B 97 155145 (2018)
  149. Richter M et al Phys. Rev. B 104 195107 (2021)
  150. Sponza L et al Phys. Rev. B 95 041112 (2017)
  151. Vučičević J et al Phys. Rev. Lett. 123 036601 (2019)
  152. Kauch A et al Phys. Rev. Lett. 124 047401 (2020)
  153. Simard O, Takayoshi S, Werner P Phys. Rev. B 103 104415 (2021)
  154. Stepanov E A et al Phys. Rev. Lett. 127 207205 (2021)
  155. Ayral T, Vučić J, Parcollet O Phys. Rev. Lett. 119 166401 (2017)
  156. Krien F Phys. Rev. B 99 235106 (2019)
  157. Stepanov E A, Harkov V, Lichtenstein A I Phys. Rev. B 100 205115 (2019)
  158. Harkov V et al Phys. Rev. B 103 245123 (2021)
  159. Stepanov E A et al Phys. Rev. B 94 205110 (2016)
  160. Krien F, Valli A, Capone M Phys. Rev. B 100 155149 (2019)
  161. Stepanov E A et al Npj Comput. Mater. 8 118 (2022)
  162. Schäfer T et al Phys. Rev. B 94 235108 (2016)
  163. Chalupa P et al Phys. Rev. B 97 245136 (2018)
  164. Krien F, Valli A Phys. Rev. B 100 245147 (2019)
  165. Vandelli M et al Phys. Rev. Res. 5 L022016 (2023)
  166. Vandelli M et al SciPost Phys. 13 036 (2022)
  167. Stepanov E A Phys. Rev. Lett. 129 096404 (2022)
  168. Bickers N E Theoretical Methods For Strongly Correlated Electrons (Eds D Sénéchal, A-M Tremblay, C Bourbonnais) (New York: Springer, 2004) p. 237-296, Ch. 6
  169. Tam K-M et al Phys. Rev. E 87 013311 (2013)
  170. Li G et al Phys. Rev. B 93 165103 (2016)
  171. Wentzell N et al Phys. Rev. B 102 085106 (2020)
  172. Eckhardt C J et al Phys. Rev. B 101 155104 (2020)
  173. Krien F et al Phys. Rev. B 102 195131 (2020)
  174. Astretsov G V, Rohringer G, Rubtsov A N Phys. Rev. B 101 075109 (2020)
  175. Taranto C et al Phys. Rev. Lett. 112 196402 (2014)
  176. Vilardi D, Taranto C, Metzner W Phys. Rev. B 99 104501 (2019)
  177. Metzner W et al Rev. Mod. Phys. 84 299 (2012)
  178. Dupuis N et al Phys. Rep. 910 1 (2021)
  179. Kugler F B, von Delft J Phys. Rev. Lett. 120 057403 (2018)
  180. Kugler F B, von Delft J Phys. Rev. B 97 035162 (2018)
  181. Hille C et al Phys. Rev. Res. 2 033068 (2020)
  182. Zhu T, Chan G K-L Phys. Rev. X 11 021006 (2021)
  183. Rubtsov A N Phys. Rev. E 97 052120 (2018)
  184. Rubtsov A N, Stepanov E A, Lichtenstein A I Phys. Rev. B 102 224423 (2020)
  185. Lyakhova Ya S, Stepanov E A, Rubtsov A N Phys. Rev. B 105 035118 (2022)
  186. Schäfer T et al Phys. Rev. X 11 011058 (2021)
© 1918–2024 Uspekhi Fizicheskikh Nauk
Email: ufn@ufn.ru Editorial office contacts About the journal Terms and conditions