Skip to main content
SpringerLink
Log in

Renormalization for Quantum Systems

  • Chapter
Real-Space Renormalization

Part of the book series: Topics in Current Physics ((TCPHY,volume 30))

Abstract

The quantum nature of physical systems shows up at very low temperatures and affects phase transition phenomena. The existence of quantum transitions at T = 0 leads to the manifestation of quantum-classical crossover phenomena in classical transitions at low temperatures. The real space renormalization group methods introduced for classical systems have been extended to quantum systems at T ≠ 0. At T = 0 a block renormalization group method has been introduced to study the ground state and the excited states of a many-body quantum system and to analyze transitions which take place in the ground state of the system. These different methods are described and discussed, giving more emphasis to the block method. The numerous applications to spin and fermion systems and to field theory in one and higher dimensions are presented.

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

Access this chapter

Log in via an institution
eBook
USD 16.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight 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

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. M.E. Fisher: Rep. Prog. Phys. 37, 617 (1967)

    Google Scholar 

  2. L. Kadanoff, W. Götze, D. Hambler, R. Hecht, E.A.S. Lewis, V.V. Polcianskas

    Google Scholar 

  3. M. Rayl, J. Swift, D.J. Kane: Rev. Mod. Phys. 39, 395 (1967)

    ADS  Google Scholar 

  4. K. Wilson, J. Kogut: Phys. Rep. 12C, 75 (1974)

    Google Scholar 

  5. L. Onsager: Phys. Rev. 65, 117 (1944)

    MathSciNet  ADS  MATH  Google Scholar 

  6. H. Stanley: Phys. Rev. 179, 570 (1969)

    ADS  Google Scholar 

  7. P. Pfeuty: Thesis, Paris (1970)

    Google Scholar 

  8. R.B. Stinchombe: J. Phys. C6, 2459 (1973)

    ADS  Google Scholar 

  9. V.G. Vaks, A.I. Larkin: JETP Sov. Phys. 22, 678 (1967)

    MathSciNet  ADS  Google Scholar 

  10. R.J. Elliott, C. Wood: J. Phys. C4, 2359 (1971)

    ADS  Google Scholar 

  11. P. Pfeuty, R.J. Elliott: J. Phys. C4, 2370 (1971)

    ADS  Google Scholar 

  12. P. Pfeuty: Ann. Phys. N.Y. 57, 79 (1970)

    ADS  Google Scholar 

  13. E. Riedel, F. Wegner: Z. Phys. 225, 195 (1969)

    ADS  Google Scholar 

  14. P. Pfeuty: J. Phys. C9, 3993 (1976)

    ADS  Google Scholar 

  15. J.A. Hertz: Phys. Rev. B14, 1165 (1976)

    ADS  Google Scholar 

  16. A.P. Young: J. Phys. C8, L309 (1975)

    ADS  Google Scholar 

  17. I.D. Lawrie: J. Phys. C11, 1123 (1978)

    ADS  Google Scholar 

  18. I.D. Lawrie, M.E. Fisher: Proc. 23rd Conference on Magnetism and Magnetic Materials, Minneapolis, 1977

    Google Scholar 

  19. Th. Niemeijer, J.M.J. Van Leeuwen: Phys. Rev. Lett. 31, 1411 (1973); Physica 16, 425 (1974)

    Google Scholar 

  20. J. Rogiers, R. Dekeyser: Phys. Rev. B13, 4886 (1976)

    ADS  Google Scholar 

  21. D.D. Betts, M. Plischke: Can. J. Phys. 54, 1553 (1976)

    ADS  Google Scholar 

  22. J. Rogiers, D.D. Betts: Physica 85A, 553 (1976)

    Google Scholar 

  23. R. Dekeyser, M. Reynaert, M.H. Lee: Physica 86–88B, 627 (1978)

    Google Scholar 

  24. A.L. Stella, F. Toigo: Phys. Rev. B17, 2343 (1978)

    ADS  Google Scholar 

  25. R. Dekeyser, M. Reynaert, A.L. Stella, F. Toigo: Phys. Rev. B18, 3486 (1978)

    ADS  Google Scholar 

  26. R.C. Brower, F. Kuttner, M. Naunberg, K. Subbarao: Phys. Rev. Lett. 38, 1231 (1977)

    ADS  Google Scholar 

  27. Z. Friedman: Phys. Rev. Lett. 36, 1326 (1976)

    ADS  Google Scholar 

  28. K. Subbarao: Phys. Rev. Lett. 37, 1712 (1976)

    ADS  Google Scholar 

  29. G. Um: Phys. Rev. B15, 2736 (1977); B17, 3670 (1978)

    Google Scholar 

  30. A.L. Stella, F. Toigo: Physica 89A, 175 (1977)

    Google Scholar 

  31. Z. Friedman: Phys. Rev. B17, 1429 (1978)

    ADS  Google Scholar 

  32. M. Suzuki, H. Takano: Phys. Lett. 69A, 426 (1979)

    Google Scholar 

  33. K. Wilson: Rev. Mod. Phys. 47, 773 (1975)

    ADS  Google Scholar 

  34. H.R. Krishna-Murthy, K.G. Wilson, J.W. Wilkins: Phys. Rev. Lett. 35, 1101 (1975)

    ADS  Google Scholar 

  35. S.D. Drell, M. Weinstein, S. Yankielowicz: Phys. Rev. D14, 487 (1976)

    ADS  Google Scholar 

  36. S.D. Drell, M. Weinstein, S. Yankielowicz: Phys. Rev. D16, 1769 (1977)

    ADS  Google Scholar 

  37. S.D. Drell, M. Weinstein: Phy s. Rev. D17, 3203 (1978)

    MathSciNet  ADS  Google Scholar 

  38. S.D. Drell, B. Svetitsky, M. Weinstein: Phys. Rev. D17, 523 (1978)

    MathSciNet  ADS  Google Scholar 

  39. B. Svetitsky, S.D. Drell, H.R. Quinn, M. Weinstein: Phys. Rev. D22, 490 (1980)

    MathSciNet  ADS  Google Scholar 

  40. D. Horn, S. Yankielowicz: Nucl. Phys. B161, 533 (1979)

    MathSciNet  ADS  Google Scholar 

  41. E. Fradkin, S. Raby: Phys. Rev. D20, 2566 (1979)

    ADS  Google Scholar 

  42. H. Hamber: Phys. Rev. D24, 941 (1981)

    ADS  Google Scholar 

  43. D. Horn, M. Karliner, S. Yankielowicz: Nucl. Phys. 8170, 467 (1980)

    ADS  Google Scholar 

  44. J. Solyom, P. Pfeuty: Phys. Rev. B24, 218 (1981)

    ADS  Google Scholar 

  45. B. Hu: Phys. Lett. 79A, 6 (1980)

    Google Scholar 

  46. R. Jullien, P. Pfeuty, J.N. Fields, S. Doniach: Phys. Rev. B18, 3568 (1978)

    ADS  Google Scholar 

  47. J. Hirsch, G. Mazenko: Phys. Rev. 819, 2656 (1979)

    Google Scholar 

  48. A. Fernandez-Pacheco: Phys. Rev. D19, 3173 (1979)

    ADS  Google Scholar 

  49. R. Jullien, K.A. Penson, P. Pfeuty: J. Phys. Paris 12, L237 (1979)

    Google Scholar 

  50. K. Penson, R. Jullien, P. Pfeuty: Phys. Rev. B19, 4653 (1979)

    ADS  Google Scholar 

  51. K. Penson, R. Jullien, P. Pfeuty: J. Phys. C12, 3667 (1979)

    Google Scholar 

  52. J. Hirsch: Phys. Rev. 820, 3907 (1979)

    Google Scholar 

  53. D.C. Mattis, J. Gallardo: J. Phys. C13, 2519 (1980)

    ADS  Google Scholar 

  54. B. Hu: Phys. Lett. 71A, 83 (1979)

    Google Scholar 

  55. K. Uzelac, P. Pfeuty, R. Jullien: Phys. Rev. Lett. 43, 805 (1979)

    ADS  Google Scholar 

  56. K. Uzelac, R. Jullien, P. Pfeuty: Phys. Rev. B22, 436 (1980)

    MathSciNet  ADS  Google Scholar 

  57. R. Jullien, K. Uzelac, P. Pfeuty, P. Moussa: J. Phys. Paris 42, 1075 (1981)

    MathSciNet  Google Scholar 

  58. K. Uzelac, K.A. Penson, R. Jullien, P. Pfeuty: J. Phys. Al2, L295 (1979)

    Google Scholar 

  59. K. Uzelac, R. Jullien, P. Pfeuty: J. Phys. A13, 3735 (1980)

    ADS  Google Scholar 

  60. K. Uzelac, R. Jullien, P. Pfeuty: J. Phys. A14, L17 (1981)

    MathSciNet  ADS  Google Scholar 

  61. H. Hamber: Phys. Rev. B21, 3999 (1980)

    ADS  Google Scholar 

  62. B. Hu: Phys. Lett. 75A, 372 (1980)

    Google Scholar 

  63. D. Boyanovsky, L. Masperi: Phys. Rev. D21, 1550 (1980)

    MathSciNet  ADS  Google Scholar 

  64. Y. Gefen, Y. Imry, D. Mukamel: Unpublished

    Google Scholar 

  65. R. Jullien, J.N. Fields, S. Doniach: Phys. Rev. Lett. 38, 1500 (1977)

    ADS  Google Scholar 

  66. R. Jullien, J.N. Fields, S. Doniach: Phys. Rev. B16, 4889 (1977)

    ADS  Google Scholar 

  67. R. Jullien, J.N. Fields, S. Doniach: Bull. Am. Phys. Soc. 22, 291 (1977)

    Google Scholar 

  68. R. Jullien, P. Pfeuty, J.N. Fields, S. Doniach: J. Phys. Paris C5 40, 293 (1979)

    Google Scholar 

  69. R. Jullien, P. Pfeuty: Phys. Rev. B19, 4646 (1979)

    ADS  Google Scholar 

  70. K.A. Penson, R. Jullien, P. Pfeuty: Phys. Rev. B22, 380 (1980)

    ADS  Google Scholar 

  71. R. Jullien, K. Penson, P. Pfeuty, K. Uzelac: Phys. Rev. Lett. 44, 1551 (1980)

    MathSciNet  ADS  Google Scholar 

  72. K.A. Penson, R. Jullien, S. Doniach, P. Pfeuty: In Ordering in Two Dimensions, ed. by S.K. Sinha ( North Holland, Amsterdam 1980 )

    Google Scholar 

  73. K.A. Penson, R. Jullien, P. Pfeuty: Phys. Rev. B (to be published)

    Google Scholar 

  74. J.N. Fields: Phys. Rev. B19, 2637 (1979)

    ADS  Google Scholar 

  75. J.N. Fields, J.C. Bonner, H.W. Blöte: J. Appl. Phys. 50, 1807 (1979)

    ADS  Google Scholar 

  76. J.M. Rabin: Phys. Rev. 821, 2027 (1980)

    Google Scholar 

  77. J.M. Rabin: Phys. Rev. B22, 2420 (1980)

    ADS  Google Scholar 

  78. J. Hirsch, J. José: J. Phys. C13, L53 (1980)

    ADS  Google Scholar 

  79. J. Hirsch, J. José: Phys. Rev. B22, 5339 (1980)

    ADS  Google Scholar 

  80. J. Hirsch: Phys. Rev. B22, 5355 (1980)

    ADS  Google Scholar 

  81. R. Jullien, P. Pfeuty, A.K. Bhattacharjee, B. Coqblin: J. Phys. Paris C5, 331 (1980)

    Google Scholar 

  82. R. Jullien, P. Pfeuty, A.K. Bhattacharjee, B. Coqblin: J. Appl. Phys. 50, 7555 (1980)

    ADS  Google Scholar 

  83. R. Jullien, P. Pfeuty, B. Coqblin: Conference on Valence Instabilities, Santa Barbara, January, 1981

    Google Scholar 

  84. R. Jullien, P. Pfeuty: J. Phys. F11, 353 (1981)

    MathSciNet  ADS  Google Scholar 

  85. C. Dasgupta, P. Pfeuty: J. Phys. C14, 717 (1981)

    ADS  Google Scholar 

  86. J. Hirsch: Phys. Rev. B22, 5259 (1980)

    MathSciNet  ADS  Google Scholar 

  87. J.G. Estëve, A.F. Pacheco, A. Sequi: Phys. Rev. D23, 1853 (1981)

    ADS  Google Scholar 

  88. G. Spronken: Thesis, Grenoble (1981)

    Google Scholar 

  89. G. Spronken, R. Jullien, M. Avignon: Phys. Rev. B24, 5356 (1981)

    ADS  Google Scholar 

  90. P. Pfeuty, R. Jullien, K.A. Penson: Unpublished

    Google Scholar 

  91. H.P. Van de Braak, W.J. Caspers, C. de Lange, M.W.M. Willanse: Physica 87A, 354 (1977)

    Google Scholar 

  92. W.J. Caspers: Phys. Rep. 63, 223 (1980)

    MathSciNet  ADS  Google Scholar 

  93. R.P. Feynmann, A.R. Hibbs: Quantum Mechanics and Path Integrals ( McGraw-Hill, New York 1965 )

    Google Scholar 

  94. R.J. Elliott, P. Pfeuty, C. Wood: Phys. Rev. Lett. 25, 443 (1970)

    ADS  Google Scholar 

  95. J. Lajzerowicz, P. Pfeuty: J. Phys. Paris C5a, 193 (1971)

    Google Scholar 

  96. M. Suzuki: Phys. Lett. 34A, 338 (1971)

    Google Scholar 

  97. M. Suzuki: Prog. Theor. Phys. 46, 1337 (1971)

    ADS  MATH  Google Scholar 

  98. M. Suzuki: Prog. Theor. Phys. 56, 1454 (1976)

    ADS  MATH  Google Scholar 

  99. E. Fradkin, L. Susskind: Phys. Rev. D17, 2637 (1978)

    MathSciNet  ADS  Google Scholar 

  100. J. Kogut: Rev. Mod. Phys. 51, 659 (1979)

    MathSciNet  ADS  Google Scholar 

  101. C.J. Hamer, M. Barber: J. Phys. A13, L169 (1980)

    ADS  Google Scholar 

  102. C.J. Hamer, M. Barber: J. Phys. A14, 241 (1981)

    MathSciNet  ADS  Google Scholar 

  103. C.J. Hamer, M. Barber: J. Phys. A14, 259 (1981)

    MathSciNet  ADS  Google Scholar 

  104. H.H. Roomany, H.W. Wyld: Phys. Rev. D21, 3341 (1980)

    MathSciNet  ADS  Google Scholar 

  105. H.H. Roomany, H.W. Wyld, L.E. Holloway: Phys. Rev. D21, 1557 (1980)

    MathSciNet  ADS  Google Scholar 

  106. H.H. Roomany, H.W. Wyld: Phys. Rev. B23, 1357 (1981)

    ADS  Google Scholar 

  107. R.R. Dos Santos, L. Sneddon: Phys. Rev. B23, 3541 (1981)

    MathSciNet  Google Scholar 

  108. K. Uzelac, R. Jullien, P. Pfeuty: J. Phys. A14, L17 (1981)

    MathSciNet  ADS  Google Scholar 

  109. M. Kolb, R. Jullien, P. Pfeuty: Unpublished

    Google Scholar 

  110. J. Hubbard: Proc. R. Soc. London A276, 238 (1963)

    ADS  Google Scholar 

  111. M. Blume, V.J. Emery, R.B. Griffiths: Phys. Rev. A4, 1071 (1971)

    ADS  Google Scholar 

  112. W. Thirring: Ann. Phys. N.Y. 3, 91 (1958)

    MathSciNet  ADS  MATH  Google Scholar 

  113. A.A. Migdal: Zh. Eksp. Teor. Fiz. 69, 810, 1457 (1975)

    Google Scholar 

  114. M. Creutz, L. Jacobs, C. Rebbi: Phys. Rev. Lett. 42, 1390 (1979)

    ADS  Google Scholar 

  115. R. Jullien, P. Pfeuty: J. Phys. A14, 3111 (1981)

    MathSciNet  ADS  Google Scholar 

  116. R. Jullien, R. Martin: Solid State Commun. (in press)

    Google Scholar 

  117. J.E. Hirsch, W. Hanke: Phys. Rev. B (in press)

    Google Scholar 

Download references

Authors
  1. P. Pfeuty
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. R. Jullien
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. K. A. Penson
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Institut Laue-Langevin, 156 X, F-38042, Grenoble Cédex, France

    Theodore W. Burkhardt

  2. Department of Physics, Temple University, 19122, Philadelphia, PA, USA

    Theodore W. Burkhardt

  3. Laboratorium voor Technische Natuurkunde, Technische Hogeschool Delft, Lorentzweg 1, 2600 GA, Delft, The Netherlands

    J. M. J. van Leeuwen

Rights and permissions

Reprints and permissions

Copyright information

© 1982 Springer-Verlag Berlin Heidelberg

About this chapter

Cite this chapter

Pfeuty, P., Jullien, R., Penson, K.A. (1982). Renormalization for Quantum Systems. In: Burkhardt, T.W., van Leeuwen, J.M.J. (eds) Real-Space Renormalization. Topics in Current Physics, vol 30. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-81825-7_5

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-81825-7_5

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-81827-1

  • Online ISBN: 978-3-642-81825-7

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation