Skip to main content
SpringerLink
Log in

The Pseudoparticle Approach to Strongly Correlated Electron Systems

  • Chapter
  • First Online:
Strongly Correlated Systems

Part of the book series: Springer Series in Solid-State Sciences ((SSSOL,volume 171))

Abstract

The most prominent pseudoparticle representations and their applications to correlated spin and electronic models are reviewed, with approximate solution schemes ranging from saddle-point approximations with Gaussian fluctuations to conserving approximations and renormalization group (RG) techniques. Merits and shortcomings of these methods are described. In particular, the generic feature of radial slave boson fields to possess a finite expectation value is discussed, while pure fluctuation fields may best be treated by conserving approximations. We present applications to the magnetic phases of the Anderson lattice model and to the Hubbard model. The noncrossing approximation and the conserving T-matrix approximation are presented and discussed as the most important conserving approximations. Furthermore RG techniques for pseudoparticle representations, including “poor man’s scaling” and functional RG for the Kondo model in and out of equilibrium, a novel RG approach to the Kondo model for strong coupling, and the functional RG approach to frustrated Heisenberg models are discussed.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 189.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 249.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 249.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Notes

  1. 1.

    We are grateful to T.A. Costi for providing the NRG data.

  2. 2.

    Note, however, that CTMA includes all potential scattering terms up to O(Γ 4).

References

  1. M. Imada, A. Fujimori, Y. Tokura, Rev. Mod. Phys. 70, 1039 (1998)

    ADS  Google Scholar 

  2. P.A. Lee, T.M. Rice, J. Serene, L.J. Sham, J.W. Wilkins, Comments on Condens. Matter Phys. 12, 99 (1986)

    Google Scholar 

  3. P. W. Anderson, Science 235, 1196 (1987); Experiment: J. G. Bednorz and K. A. Müller, Z. Physik B 64, 189 (1986); B. Raveau, C. Michel, M. Hervieu, D. Groult, A. Maignan, J. Provost, J. Supercond. 5, 203 (1992)

    Google Scholar 

  4. A.C. Hewson, The Kondo Problem to Heavy Fermions (Cambridge University Press, London, 1993)

    Google Scholar 

  5. T. Holstein, H. Primakoff, Phys. Rev. 58, 1094 (1940)

    ADS  Google Scholar 

  6. J. Schwinger, in Quantum Theory of Angular Momentum, ed. by H. Biedenharn, H. Van Dam (Academic, New York, 1965)

    Google Scholar 

  7. A.A. Abrikosov, Physics (Long Island City, N.Y.) 2, 5 (1965)

    Google Scholar 

  8. B. Coqblin, J.R. Schrieffer, Phys. Rev. 185, 847 (1969)

    ADS  Google Scholar 

  9. S.E. Barnes, J. Phys. F 6, 1375 (1976); 7, 2637 (1977)

    Google Scholar 

  10. P. Coleman, Phys. Rev. B 29, 3035 (1984)

    ADS  Google Scholar 

  11. M. Gutzwiller, Phys. Rev. Lett. 10, 159 (1963)

    ADS  Google Scholar 

  12. G. Kotliar, A.E. Ruckenstein, Phys. Rev. Lett. 57, 1362 (1986)

    MathSciNet  ADS  Google Scholar 

  13. T.C. Li, P. Wölfle, P.J. Hirschfeld, Phys. Rev. B 40, 6817 (1989)

    ADS  Google Scholar 

  14. R. Frésard, P. Wölfle, Int. J. of Mod. Phys. B 6, 685 (1992); ibid., p. 3087 (1992)

    Google Scholar 

  15. R. Frésard, G. Kotliar, Phys. Rev. B 56, 12 909 (1997)

    Google Scholar 

  16. F. Lechermann, A. Georges, G. Kotliar, O. Parcollet, Phys. Rev. B 76, 155102 (2007)

    ADS  Google Scholar 

  17. U. Larsen, Z. Physik 256, 65 (1972)

    ADS  Google Scholar 

  18. V.N. Popov, S.A. Fedotov, Sov. Phys. JETP 67, 535 (1988)

    Google Scholar 

  19. J. Brinckmann, P. Wölfle, Physica B 359–361, 798 (2005)

    Google Scholar 

  20. M.N. Kiselev, R. Oppermann, JETP Lett. 71, 250 (2000)

    ADS  Google Scholar 

  21. R. Dillenschneider, J. Richert, Phys. Rev. B 73, 024409 (2006)

    ADS  Google Scholar 

  22. J. Reuther, P. Wölfle, Phys. Rev. B 81, 144410 (2010)

    ADS  Google Scholar 

  23. J. Kroha, P. Hirschfeld, K.A. Muttalib, P. Wölfle Solid State Comm. 83 (12), 1003 (1992)

    ADS  Google Scholar 

  24. N. Read, D.M. Newns, J. Phys. C 16, L1055 (1983)

    ADS  Google Scholar 

  25. N. Read, D.M. Newns, J. Phys. C 16, 3273 (1983)

    ADS  Google Scholar 

  26. D.M. Newns, N. Read, Adv. Phys. 36, 799 (1987)

    ADS  Google Scholar 

  27. R. Frésard, T. Kopp, Nucl. Phys. B 594, 769 (2001)

    ADS  Google Scholar 

  28. R. Frésard, H. Ouerdane, T. Kopp, Nucl. Phys. B 785, 286 (2007)

    ADS  MATH  Google Scholar 

  29. J.W. Rasul, T. Li, J. Phys. C 21, 5119 (1988)

    ADS  Google Scholar 

  30. T.C. Li, J.W. Rasul, Phys. Rev. B 39, 4630 (1989)

    ADS  Google Scholar 

  31. J.W. Rasul, T.C. Li, H. Beck, Phys. Rev. B 39, 4191 (1989)

    ADS  Google Scholar 

  32. M. Lavagna, Phys. Rev. B 41, 142 (1990); Helvetica Physica Acta 63, 310 (1990); Int. J. Mod. Phys. B 5, 885 (1991)

    Google Scholar 

  33. Th. Jolicœur and J.C. Le Guillou, Phys. Rev. B 44, 2403 (1991)

    ADS  Google Scholar 

  34. Y. Bang, C. Castellani, M. Grilli, G. Kotliar, R. Raimondi, Z. Wang, Int. J. Mod. Phys. B 6, 531 (1992)

    ADS  Google Scholar 

  35. R. Frésard, T. Kopp, Phys. Rev. B. 78, 073108 (2008)

    ADS  Google Scholar 

  36. W. Zimmermann, R. Frésard, P. Wölfle, Phys. Rev. B 56, 10 097 (1997)

    Google Scholar 

  37. B. Möller, K. Doll, R. Frésard, J. Phys. Condens. Matter 5 4847 (1993)

    ADS  Google Scholar 

  38. R. Frésard, M. Dzierzawa, P. Wölfle, Europhys. Lett. 15, 325 (1991)

    ADS  Google Scholar 

  39. E. Arrigoni, G.C. Strinati, Phys. Rev. B 44, 7455 (1991)

    ADS  Google Scholar 

  40. R. Frésard, P. Wölfle, J. Phys. Condens. Matter 4 3625 (1992)

    ADS  Google Scholar 

  41. G. Seibold, E. Sigmund, V. Hizhnyakov, Phys. Rev. B 57, 6937 (1998)

    ADS  Google Scholar 

  42. M. Raczkowski, R. Frésard, A.M. Oleś, Phys. Rev. B 73, 174525 (2006)

    ADS  Google Scholar 

  43. M. Raczkowski, R. Frésard, A.M. Oleś, Europhys. Lett. 76, 128 (2006)

    ADS  Google Scholar 

  44. A. Isidori, M. Capone, Phys. Rev. B 80, 115120 (2009)

    ADS  Google Scholar 

  45. A. Ruegg, S. Pilgram, M. Sigrist, Phys. Rev. B 75, 195117 (2007)

    ADS  Google Scholar 

  46. P. Korbel, W. Wojcik, A. Klejnberg, J. Spałek, M. Acquarone, M. Lavagna, Eur. Phys. J. B 32, 315 (2003)

    ADS  Google Scholar 

  47. G. Kotliar, E. Lange, M.J. Rozenberg, Phys. Rev. Lett. 84, 5180 (2000)

    ADS  Google Scholar 

  48. G. Seibold, Phys. Rev. B 58, 15520 (1998)

    ADS  Google Scholar 

  49. J. Lorenzana, G. Seibold, Low Temp. Phys. 32, 320 (2006)

    ADS  Google Scholar 

  50. W.F. Brinkman, T.M. Rice, Phys. Rev. B. 2, 4302 (1970)

    ADS  Google Scholar 

  51. D. Vollhardt, Rev. Mod. Phys. 56, 99 (1984)

    ADS  Google Scholar 

  52. D. Vollhardt, P. Wölfle, P.W. Anderson, Phys. Rev. B. 35, 6703 (1987)

    ADS  Google Scholar 

  53. S. Doniach, Physica B, C 91, 231 (1977)

    Google Scholar 

  54. H.v. Löhneysen, A. Rosch, M. Vojta, P. Wölfle, Rev. Mod. Phys. 79, 1015 (2007)

    Google Scholar 

  55. B. Möller, P. Wölfle, Phys. Rev. B 48, 10320 (1993)

    Google Scholar 

  56. M. Guerrero, R.M. Noack, Phys. Rev. B 53, 3707 (1996)

    ADS  Google Scholar 

  57. T.C. Li, Y.S. Sun, P. Wölfle, Z. Phys. B Condens. Matter 82, 369 (1991)

    ADS  Google Scholar 

  58. T.C. Li, P. Bénard, Phys. Rev. B. 50, 17 387 (1994)

    Google Scholar 

  59. P. Limelette, H. Muguerra, S. Hébert, Phys. Rev. B 82, 035123 (2010)

    ADS  Google Scholar 

  60. K. Doll, M. Dzierzawa, R. Frésard, P. Wölfle, Z. Phys. B Condens. Matter 90, 297 (1993)

    ADS  Google Scholar 

  61. R. Frésard, W. Zimmermann, Phys. Rev. B 58, 15288 (1998)

    ADS  Google Scholar 

  62. M. Dzierzawa, unpublished

    Google Scholar 

  63. G. Baym, L.P. Kadanoff, Phys. Rev. 124 (1961) 287

    MathSciNet  ADS  MATH  Google Scholar 

  64. G. Baym, Phys. Rev. 127, 1391 (1962)

    MathSciNet  ADS  MATH  Google Scholar 

  65. P.W. Anderson, Phys. Rev. Lett. 18, 1049 (1967); Phys. Rev. 164, 352 (1967)

    Google Scholar 

  66. B. Menge, E. Müller-Hartmann, Z. Phys. B 73, 225 (1988)

    ADS  Google Scholar 

  67. J. Kroha, P. Wölfle, T.A. Costi, Phys. Rev. Lett. 79, 261 (1997)

    ADS  Google Scholar 

  68. J. Kroha, P. Wölfle, J. Phys. Soc. Jpn. 74 (1), 16 (2005)

    ADS  Google Scholar 

  69. T.A. Costi, P. Schmitteckert, J. Kroha, P. Wölfle, Phys. Rev. Lett. 73, 1275 (1994); Physica C235–240, 2287 (1994)

    Google Scholar 

  70. E. Müller-Hartmann, Z. Physik B 57, 281 (1984)

    Google Scholar 

  71. Y. Kuramoto, E. Müller-Hartmann, J. Mag. Mag. Mat. 52, 122 (1985)

    ADS  Google Scholar 

  72. J. Brinckmann, P. Wölfle, Phys. Rev. B 70, 174445 (2004)

    ADS  Google Scholar 

  73. H. Keiter, J.C. Kimball, Int. J. Magn. 1 233 (1971)

    Google Scholar 

  74. N. Grewe, H. Keiter, Phys. Rev. B 24 4420 (1981)

    ADS  Google Scholar 

  75. Y. Kuramoto, Z. Physik B 53, 37 (1983)

    ADS  Google Scholar 

  76. H. Kojima, Y. Kuramoto, and M. Tachiki, Z. Physik B 54, 293 (1984)

    Google Scholar 

  77. Y. Kuramoto, H. Kojima, Z. Physik 57, 95 (1984)

    ADS  Google Scholar 

  78. Y. Kuramoto, Z. Physik B 65, 29 (1986)

    Google Scholar 

  79. N.E. Bickers, D.L. Cox, J.W. Wilkins, Phys. Rev. B 36, 2036 (1987)

    Google Scholar 

  80. N.E. Bickers, Rev. Mod. Phys. 59, 845 (1987)

    ADS  Google Scholar 

  81. T.A. Costi, J. Kroha, P. Wölfle, Phys. Rev. B 53, 1850 (1996)

    Google Scholar 

  82. P. Nozières, A. Blandin, J. Phys. (Paris) 41, 193 (1980)

    Google Scholar 

  83. K. Haule, A. Rosch, J. Kroha, P. Wölfle, Phys. Rev. Lett. 89, 236402 (2002)

    ADS  Google Scholar 

  84. K. Haule, A. Rosch, J. Kroha, P. Wölfle, Phys. Rev. B 68, 155119 (2003)

    ADS  Google Scholar 

  85. F. B. Anders, M. Jarrel, D. Cox, Phys. Rev. Lett. 78, 2000 (1997)

    ADS  Google Scholar 

  86. A. Schiller, F. B. Anders, D. Cox, Phys. Rev. Lett. 81, 3235 (1998)

    ADS  Google Scholar 

  87. M. Arnold, J. Kroha, Phys. Rev. Lett. 100, 046404 (2008)

    ADS  Google Scholar 

  88. F. Reinert et al., Phys. Rev. Lett. 87, 106401 (2001)

    MathSciNet  ADS  Google Scholar 

  89. D. Ehm et al., Phys. Rev. B 76, 045117 (2007)

    ADS  Google Scholar 

  90. D.L. Cox, A.R. Ruckenstein, Phys. Rev. Lett. 71, 1613 (1993)

    ADS  Google Scholar 

  91. S. Kirchner, J. Kroha, J. Low Temp. Phys. 126, 1233 (2002)

    Google Scholar 

  92. J.R. Schrieffer, P.A. Wolff, Phys. Rev. 149, 491 (1966)

    ADS  Google Scholar 

  93. K. Haule, S. Kirchner, J. Kroha, P. Wölfle: Phys. Rev. B 64, 155111 (2001)

    ADS  Google Scholar 

  94. J. Holm, K. Schönhammer, Solid State Comm. 69, 969 (1989)

    ADS  Google Scholar 

  95. O. Sakai, M. Motizuki, T. Kasuya, Springer Series in Solid-State Sciences, vol. 81 (Springer, Berlin, 1988), p. 45

    Google Scholar 

  96. Th. Pruschke, N. Grewe, Z. Phys. B 74, 439 (1989)

    ADS  Google Scholar 

  97. F.B. Anders, N. Grewe, Europhys. Lett. 26, 551 (1994)

    ADS  Google Scholar 

  98. J. Kroha, P. Wölfle, in Theoretical Methods for Strongly Correlated Electrons, CRM Series in Mathematical Physics (Springer, New York, 2003), p. 297

    Google Scholar 

  99. S. Kirchner, J. Kroha, P. Wölfle, Phys. Rev. B 70, 165102 (2004)

    ADS  Google Scholar 

  100. H. Keiter, K. Baumgartner, Phys. Stat. Sol. (b) 242(2), 377 (2005)

    Google Scholar 

  101. H. Keiter, K. Baumgartner, S. Duffe, Phys. Stat. Sol. (b) 244 (7), 2357 (2007)

    Google Scholar 

  102. J. Kroha, P. Wölfle, unpublished

    Google Scholar 

  103. P.W. Anderson, J. Phys. C 3, 2439 (1970)

    ADS  Google Scholar 

  104. K.G. Wilson, Rev. Mod. Phys. 47, 773  (1975)

    ADS  Google Scholar 

  105. D. Goldhaber-Gordon et al., Nature (London) 391, 156 (1998)

    Google Scholar 

  106. S.M. Cronenwett, T.H. Oosterkamp, L.P. Kouwenhoven, Science 281, 540 (1998)

    ADS  Google Scholar 

  107. A. Rosch, J. Paaske, J. Kroha, P. Wölfle, Phys. Rev. Lett. 90, 076804 (2003)

    ADS  Google Scholar 

  108. A. Rosch, J. Paaske, J. Kroha, P. Wölfle, J. Phys. Soc. Jpn. 74, 118 (2005)

    ADS  MATH  Google Scholar 

  109. J. Paaske, A. Rosch, P. Wölfle, Phys. Rev. B 69, 155330 (2004)

    ADS  Google Scholar 

  110. J. Paaske, A. Rosch, J. Kroha, P. Wölfle, Phys. Rev. B 70, 155301 (2004)

    ADS  Google Scholar 

  111. H. Schmidt, P. Wölfle, Ann. Phys. (Berlin) 19, 60 (2010)

    ADS  MATH  Google Scholar 

  112. A. Rosch, J. Kroha, P. Wölfle, Phys. Rev. Lett. 57, 156802 (2003)

    Google Scholar 

  113. J. Paaske, A. Rosch, P. Wölfle, C.M. Marcus, J. Nygård, Nat. Phys. 2, 460 (2006)

    Google Scholar 

  114. V. Koerting, P. Wölfle, J. Paaske, Phys. Rev. Lett. 99, 036807 (2007)

    ADS  Google Scholar 

  115. V. Koerting, J. Paaske, P. Wölfle, Phys. Rev. B 77, 165122 (2008)

    ADS  Google Scholar 

  116. S. Schmaus, V. Koerting, J. Paaske, T.S. Jespersen, J. Nygård, P. Wölfle, Phys. Rev. B 79, 045105 (2009)

    ADS  Google Scholar 

  117. C.-H. Chung, G. Zarand, P. Wölfle, Phys. Rev. 77, 035120 (2008)

    ADS  Google Scholar 

  118. C.-H. Chung, K. LeHur, M. Vojta, P. Wölfle, Phys. Rev. Lett. 102, 216803 (2009)

    ADS  Google Scholar 

  119. U. Larsen, R.D. Mattuck, Proceedings of the International Conference on Magnetism, Moscow, U.S.S.R., 1973, vol. 5 (Nauka, Moscow, 1974), p. 88

    Google Scholar 

  120. U. Larsen, Phys. Lett. A 40, 39 (1972)

    ADS  Google Scholar 

  121. J. Paaske, H. Schmidt, P. Wölfle, to be published (2011)

    Google Scholar 

  122. M. Salmhofer, Renormalization: An Introduction (Springer, Berlin, 1998)

    Google Scholar 

  123. V. Meden, Advances in Solid State Physics, vol. 46, ed. by R. Haug (Springer, New York, 2007)

    Google Scholar 

  124. W. Metzner, in Functional Renormalization Group Aapproach to Interacting Systems. Lecture Notes in Physics (Springer, Berlin, 2007)

    Google Scholar 

  125. A.A. Katanin, Phys. Rev. 70, 115109 (2004)

    ADS  Google Scholar 

  126. J. Reuther, P. Wölfle, R. Darradi, W. Brenig, M. Arlego, J. Richter, Phys. Rev. B 83, 064416 (2011)

    ADS  Google Scholar 

Download references

Acknowledgments

We thank Jan Brinckmann, Theo Costi, Klaus Doll, Michael Dzierzawa, Peter Hirschfeld, Stefan Kirchner, Thilo Kopp, Gabi Kotliar, Burkhard Möller, Kandkher Muttalib, Andrzej Oleś, Henni Ouerdane, Jens Paaske, Marcin Raczkowski, Johannes Reuther, Achim Rosch, Holger Schmidt, and Walter Zimmermann for valuable collaboration. RF gratefully acknowledges financial support by the Région Basse-Normandie and the Ministère de la Recherche. JK is grateful for financial support from the Deutsche Forschungsgemeinschaft through SFB 608 and through grant No. KR 1727/1-2 and PW acknowledges support through the DFG Research Center for Functional Nanostructures (CFN) and the DFG Research Unit 960 “Quantum Phase Transitions”.

Author information

Authors and Affiliations

  1. Laboratoire Crismat, UMR CNRS-ENSICAEN(ISMRA) 6508, 6, Bld. du Marèchal Juin, 14050, Caen CEDEX 4, France

    Raymond Frésard

  2. Physikalisches Institut, Universität Bonn, 53115, Bonn, Germany

    Johann Kroha

  3. Institut für Theorie der Kondensierten Materie and Institut für Nanotechnologie, Karlsruher Institut für Technologie (KIT), 76049, Karlsruhe, Germany

    Peter Wölfle

Authors
  1. Raymond Frésard
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Johann Kroha
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Peter Wölfle
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Raymond Frésard .

Editor information

Editors and Affiliations

  1. Dipartimento di Fisica "E.R. Caianiello", Università degli Studi di Salerno, Via Ponte don Melillo, Fisciano (SA), 84084, Italy

    Adolfo Avella

  2. Dipartimento di Fisica "E.R. Caianiello", Università degli Studi di Salerno, Via Ponte don Melillo, Fisciano (SA), 84084, Italy

    Ferdinando Mancini

Rights and permissions

Reprints and permissions

Copyright information

© 2012 Springer-Verlag Berlin Heidelberg

About this chapter

Cite this chapter

Frésard, R., Kroha, J., Wölfle, P. (2012). The Pseudoparticle Approach to Strongly Correlated Electron Systems. In: Avella, A., Mancini, F. (eds) Strongly Correlated Systems. Springer Series in Solid-State Sciences, vol 171. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-21831-6_3

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-21831-6_3

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-21830-9

  • Online ISBN: 978-3-642-21831-6

  • eBook Packages: Physics and AstronomyPhysics and Astronomy (R0)

Publish with us

Policies and ethics

Search

Navigation