Issues

 / 

2005

 / 

September

  



Diagrammatic Monte Carlo method as applied to the polaron problems


Cross-Correlated Materials Research Group (CMRG), ASI, RIKEN, Wako, Saitama , Japan

Numerical methods whereby exact solutions to the problem of a few particles interacting with one another and with several bosonic excitation branches are presented. The diagrammatic Monte Carlo method allows the exact calculation of the Matsubara Green function, and the stochastic optimization technique provides an approximation-free analytic continuation. In this review, results unobtainable by conventional methods are discussed, including the properties of excited states in the self-trapping phenomenon, the optical spectra of polarons in all coupling regimes, the validity range analysis of the Frenkel and Wannier approximations relevant to the exciton, and the peculiarities of photoemission spectra of a lattice- coupled hole in a Mott insulator.

Fulltext is available at IOP
PACS: 02.70.Uu, 71.35.−y, 71.38.−k, 74.72.−h (all)
DOI: 10.1070/PU2005v048n09ABEH002632
URL: https://ufn.ru/en/articles/2005/9/b/
Citation: Mishchenko A S "Diagrammatic Monte Carlo method as applied to the polaron problems" Phys. Usp. 48 887–902 (2005)
BibTexBibNote ® (generic)BibNote ® (RIS)MedlineRefWorks

Оригинал: Мищенко А С «Диаграммный метод Монте-Карло в применении к проблемам поляронов» УФН 175 925–942 (2005); DOI: 10.3367/UFNr.0175.200509b.0925

References (109) ↓ Cited by (21)

  1. Appel J In Solid State Physics Vol. 21 (Eds H Ehrenreich, F Seitz, D Turnbull) (New York: Academic Press, 1968)
  2. Firsov Yu A Polyarony (M.: Nauka, 1975)
  3. Kane C L, Lee P A, Read N Phys. Rev. B 39 6880 (1989)
  4. Izyumov Yu A Usp. Fiz. Nauk 167 465 (1997); Izyumov Yu A Phys. Usp. 40 445 (1997)
  5. Ansel’m A I, Firsov Yu A Zh. Eksp. Teor. Fiz. 28 151 (1955); Ansel’m A I, Firsov Yu A Zh. Eksp. Teor. Fiz. 30 719 (1956); Toyozawa Y Prog. Theor. Phys. 20 53 (1958)
  6. Davydov A S Teoriya Tverdogo Tela (M.: Nauka, 1976)
  7. Toyozawa Y Optical Processes In Solids (Cambridge: Cambridge Univ. Press, 2003)
  8. Devreese J T In Encyclopedia Of Applied Physics Vol. 14 (Ed. G L Trigg) (New York: VCH Publ., 1996) p. 383
  9. Landau L Phys. Z. Sowjetunion 3 664 (1933)
  10. Fröhlich H, Pelzer H, Zienau S Philos. Mag. 41 221 (1950)
  11. Kanamori J Appl. Phys. Suppl. 31 S14 (1960); Abragam A, Bleaney B Electron Paramagnetic Resonance Of Transition Ions (Oxford: Clarendon Press, 1970); Kugel’ K I, Khomskii D I Usp. Fiz. Nauk 136 621 (1982); Kugel’ K I, Khomskii D I Sov. Phys. Usp. 25 231 (1982)
  12. Davydov A S Teoriya Pogloshcheniya Sveta v Molekulyarnykh Kristallakh (Kiev: Izd-vo AN USSR, 1951); Ray E G Austr. J. Chem. 16 315 (1963)
  13. Rashba E I Zh. Eksp. Teor. Fiz. 50 1064 (1966); Rashba E I Zh. Eksp. Teor. Fiz. 54 542 (1968)
  14. Bersuker I B, Polinger V Z Vibronnye Vzaimodeistviya v Molekulakh i Kristallakh (M.: Nauka, 1983)
  15. Pekar S I Issledovaniya Po Elektronnoi Teorii Kristallov (M.: Gostekhizdat, 1951)
  16. Schultz T D In Polarons And Excitons (Eds C G Kuper, G D Whitfield) (Edinburgh: Oliver and Boyd, 1963) p. 71
  17. Vinnitskii V L Zh. Eksp. Teor. Fiz. 40 1459 (1961); Anderson P W Phys. Rev. Lett. 34 953 (1975); Rice T M, Sneddon L Phys. Rev. Lett. 47 689 (1981)
  18. Sumi A J. Phys. Soc. Jpn. 43 1286 (1977)
  19. Ueta M et al. Excitonic Processes In Solids (Springer Ser. In Solid-State Sci., Vol. 60) (Berlin: Springer-Verlag, 1986)
  20. Shinozuka Y, Toyozawa Y J. Phys. Soc. Jpn. 46 505 (1979); Toyozawa Y Physica B+C 116 7 (1983)
  21. Knox R S Theory Of Excitons (New York: Academic Press, 1963)
  22. Egri I Phys. Rep. 119 363 (1985)
  23. Haarer D Chem. Phys. Lett. 31 192 (1975); Haarer D, Philpott M R, Morawitz H J. Chem. Phys. 63 5238 (1975); Elschner A, Weiser G Chem. Phys. 98 465 (1985)
  24. Prokof ’ev N V, Svistunov B V, Tupitsyn I S Zh. Eksp. Teor. Fiz. 114 570 (1998)
  25. Prokof ’ev N V, Svistunov B V Phys. Rev. Lett. 81 2514 (1998)
  26. Mishchenko A S et al. Phys. Rev. B 62 6317 (2000)
  27. Mishchenko A S, Nagaosa N Phys. Rev. Lett. 86 4624 (2001)
  28. Mishchenko A S, Prokof ’ev N V, Svistunov B V Phys. Rev. B 64 033101 (2001)
  29. Burovski E A et al. Phys. Rev. Lett. 87 186402 (2001)
  30. Mishchenko A S et al. Nonlinear Opt. 29 257 (2002)
  31. Mishchenko A S et al. Phys. Rev. Lett. 91 236401 (2003)
  32. Mishchenko A S, Nagaosa N Phys. Rev. Lett. 93 036402 (2004)
  33. Abrikosov A A, Gor’kov L P, Dzyaloshinskii I E Metody Kvantovoi Teorii Polya v Statisticheskoi Fizike (M.: Dobrosvet, 1998)
  34. Mahan G D Many-Particle Physics 3rd ed. (New York: Kluwer Acad./Plenum Publ., 2000)
  35. Jarrell M, Gubernatis J E Phys. Rep. 269 133 (1996)
  36. Kress R Linear Integral Systems 2nd ed. (New York: Springer, 1999)
  37. Metropolis N et al. J. Chem. Phys. 21 1087 (1953)
  38. Landau D P, Binder K A Guide To Monte Carlo Simulations In Statistical Physics (Cambridge: Cambridge Univ. Press, 2000)
  39. Sandvik A W, Kurkijärvi J Phys. Rev. B 43 5950 (1991)
  40. Tikhonov A N, Arsenin V Y Solutions Of Ill-Posed Problems (Washington: Winston, 1977); Tikhonov A N, Arsenin V Ya Metody Resheniya Nekorrektnykh Zadach 3-e izd. (M.: Nauka, 1986)
  41. Perchik E math-ph/0302045
  42. Phillips D L J. Assoc. Comput. Mach. 9 84 (1962)
  43. Tikhonov A N Dokl. Akad. Nauk SSSR 151 501 (1963)
  44. Mishchenko A S et al. Phys. Rev. B 66 020301(R) (2002)
  45. Aplesnin S S Zh. Eksp. Teor. Fiz. 124 1080 (2003)
  46. Frenkel J Phys. Rev. 37 17 (1931)
  47. Wannier G H Phys. Rev. 52 191 (1937)
  48. Onida G, Reining L, Rubio A Rev. Mod. Phys. 74 601 (2002)
  49. Albrecht S et al. Phys. Rev. Lett. 80 4510 (1998); Benedict L X, Shirley E L, Bohn R B Phys. Rev. Lett. 80 4514 (1998)
  50. Rohlfing M, Louie S G Phys. Rev. Lett. 81 2312 (1998)
  51. Marini A, Del Sole R Phys. Rev. Lett. 91 176402 (2003)
  52. Devreese J, Evrard R Phys. Lett. 11 278 (1964)
  53. Kartheuser E, Evrard R, Devreese J Phys. Rev. Lett. 22 94 (1969)
  54. Devreese J, De Sitter J, Goovaerts M Phys. Rev. B 5 2367 (1972)
  55. Devreese J T In Polarons In Ionic Crystals And Polar Semiconductors (Ed. J T Devreese) (Amsterdam: North-Holland, 1972) p. 83
  56. Mishchenko A S et al. in Proc. of 2000 Intern. Conf. on Excitonic Processes of Condensed Matter, Osaka, Japan, August 22 - 25, 2000 (Eds K Cho, A Matsui) (Singapore: World Scientific, 2001) p. 372
  57. Lee T D, Low F E, Pines D Phys. Rev. 90 297 (1953)
  58. Rashba E I In Modern Problems In Condensed Matter Sciences Vol. 2 (Eds V M Agranovich, A A Maradudin) (Amsterdam: Notrh-Holland, 1982) p. 543; Ioselevich A S, Rashba E I In Modern Problems In Condensed Matter Sciences Vol. 34 (Eds V M Agranovich, A A Maradudin) (Amsterdam: Notrh-Holland, 1992) p. 347
  59. Stephan W Phys. Rev. B 54 8981 (1996)
  60. Wellein G, Fehske H Phys. Rev. B 56 4513 (1997)
  61. Fehske H, Loos J, Wellein G Z. Phys. B 104 619 (1997)
  62. Fehske H, Loos J, Wellein G Phys. Rev. B 61 8016 (2000)
  63. Bonča J, Trugman S A, Batistić I Phys. Rev. B 60 1633 (1999)
  64. Ku L-C, Trugman S A, Bonča J Phys. Rev. B 65 174306 (2002)
  65. Shawish S E et al. Phys. Rev. B 67 014301 (2003)
  66. Barišić O S Phys. Rev. B 65 144301 (2002)
  67. Barišić O S Phys. Rev. B 69 064302 (2004)
  68. Sénéchal D, Perez D, Pioro-Landrière M Phys. Rev. Lett. 84 522 (2000); Sénéchal D, Perez D, Plouffe D Phys. Rev. B 66 075129 (2002)
  69. Hohenadler M, Aichhorn M, von der Linden W Phys. Rev. B 68 184304 (2003)
  70. Gerlach B, Löwen H Rev. Mod. Phys. 63 63 (1991)
  71. Pekar S I, Rashba E I, Shcheka V I Zh. Eksp. Teor. Fiz. 76 251 (1979)
  72. Dykman I M, Pekar S I Dokl. Akad. Nauk SSSR 83 825 (1952)
  73. Mishchenko A S, Nagaosa N in Proc. of 2000 Intern. Conf. on Excitonic Processes of Condensed Matter, Osaka, Japan, August 22 - 25, 2000 (Eds K Cho, A Matsui) (Singapore: World Scientific, 2001) p. 105
  74. Kikoin K A, Mishchenko A S Zh. Eksp. Teor. Fiz. 104 3810 (1993)
  75. Feynman R P et al. Phys. Rev. 127 1004 (1962)
  76. Pitaevskii L P Zh. Eksp. Teor. Fiz. 36 1168 (1959)
  77. Curnoe S, Kikoin K A Phys. Rev. B 61 15714 (2000)
  78. Kikoin K A, Mishchenko A S Zh. Eksp. Teor. Fiz. 94 (11) 237 (1988)
  79. Kikoin K A, Mishchenko A S J. Phys. Condens. Matter 2 6491 (1990)
  80. Alekseev P A et al. Europhys. Lett. 10 457 (1989)
  81. Mishchenko A S, Kikoin K A J. Phys. Condens. Matter 3 5937 (1991)
  82. Travaglini G, Wachter P Phys. Rev. B 29 893 (1984)
  83. Lemmens P et al. Physica B 206 - 207 371 (1995)
  84. Kikoin K A, Mishchenko A S J. Phys. Condens. Matter 7 307 (1995)
  85. Kasuya T Europhys. Lett. 26 277 (1994); Kasuya T Europhys. Lett. 26 283 (1994)
  86. Manousakis E Rev. Mod. Phys. 63 1 (1991); Dagotto E Rev. Mod. Phys 66 763 (1994)
  87. Brunner M, Assaad F F, Muramatsu A Phys. Rev. B 62 15480 (2000)
  88. Belinicher V I, Chernyshev A L, Shubin V A Phys. Rev. B 53 335 (1996); Belinicher V I, Chernyshev A L, Shubin V A Phys. Rev. B 54 14914 (1996)
  89. Xiang T, Wheatley J M Phys. Rev. B 54 R12653 (1996)
  90. Kyung B, Ferrell R A Phys. Rev. B 54 10125 (1996)
  91. Lee T K, Shih C T Phys. Rev. B 55 5983 (1997)
  92. Lee T K, Ho C-M, Nagaosa N Phys. Rev. Lett. 90 067001 (2003)
  93. Tohyama T, Maekawa S Supercond. Sci. Technol. 13 R17 (2000)
  94. Damascelli A, Hussain Z, Shen Z-X Rev. Mod. Phys. 75 473 (2003)
  95. Wells B O et al. Phys. Rev. Lett. 74 964 (1995)
  96. Bała J, Oleś A M, Zaanen J Phys. Rev. B 52 4597 (1995)
  97. Horsch P, Khaliullin G In Open Problems In Strongly Correlated Electron Systems (NATO Sci. Ser., Ser. II, Vol. 15, Eds J Bonca Et Al.) (Boston: Kluwer-Acad. Publ., 2000) p. 117; Horsch P, Khaliullin G, Oudovenko V Physica C 341 - 348 117 (2000)
  98. Rösch O, Gunnarsson O Phys. Rev. Lett. 92 146403 (2004)
  99. Rösch O, Gunnarsson O Phys. Rev. Lett. 93 237001 (2004)
  100. McQueeney R J et al. Phys. Rev. B 54 R9689 (1996); McQueeney R J et al. Phys. Rev. Lett. 82 628 (1999); Pintschovius L, Braden M Phys. Rev. B 60 R15039 (1999)
  101. Hofer J et al. Phys. Rev. Lett. 84 4192 (2000)
  102. Bernhard C et al. Phys. Rev. B 69 052502 (2004)
  103. Gweon G-H et al. Nature 430 187 (2004)
  104. Liu Z, Manousakis E Phys. Rev. B 45 2425 (1992)
  105. Ramsak A, Horsch P, Fulde P Phys. Rev. B 46 14305 (1992); Kyung B et al. Phys. Rev. B 54 13167 (1996); Mukhin S I Phys. Rev. B 55 3886 (1997)
  106. Marsiglio F et al. Phys. Rev. B 43 10882 (1991)
  107. Shen K M et al. Phys. Rev. Lett. 93 267002 (2004)
  108. Macridin A, Sawatzky G A, Jarrell M Phys. Rev. B 69 245111 (2004)
  109. Toyozawa Y Prog. Theor. Phys. 26 29 (1961)

© 1918–2020 Uspekhi Fizicheskikh Nauk
Email: ufn@ufn.ru Editorial office contacts About the journal Terms and conditions