Skip to main content
SpringerLink
Log in

Frustrated Quantum Magnets

  • Chapter
  • First Online:
High Magnetic Fields

Part of the book series: Lecture Notes in Physics ((LNP,volume 595))

Abstract

In these lectures we present a summary of the T = 0 properties of the ground state and first excitations of two-dimensional frustrated quantum magnets. Up to now four phases have been observed at T = 0: a Néel ordered phase with spontaneous symmetry breaking and soft modes (the antiferromagnetic magnons) and three phases with no SU(2) symmetry breaking and a spin gap. The first four sections are devoted to the characterization of these four phases. We first explain the two main quantum effects which can take place in the semi-classical Néel phase: reduction of the order parameter by quantum fluctuations and in the case of a competition between various ordered phases: selection of the most symmetric one by quantum fluctuations. Amongst the three spin gapped phases, the Valence Bond Crystal has long range order in S = 0 valence bonds and all its excitations have integer spins. The other two, the Resonating Valence Bond Spin Liquids have no local order parameter and fractionalized excitations. After a characterization of these different phases we use information gathered from exact diagonalizations, toy models and large N expansions to emphasize criteria that seem important to find one or another of these spin gapped phases. The last section of this paper is concerned with the special behavior of frustrated magnets in high magnetic fields: metamagnetic behavior and quantized plateaus. Some insights are given on Chiral Spin Liquids and on a proposed connexion between Quantum Hall Effect and magnetization plateaus.

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 84.99
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
Hardcover Book
USD 109.99
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

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. N.D. Mermin, H. Wagner: Phys. Rev. Lett. 17, 1133 (1966)

    Article  ADS  Google Scholar 

  2. D.C. Mattis: The Theory of Magnetism I, Vol. 17 of Springer Series in Solid-State Sciences (Springer-Verlag, Berlin, Heidelberg, New York, Tokyo, 1981)

    Google Scholar 

  3. W.J. Caspers: Spin Systems (World Scientific, Singapore, 1989)

    Google Scholar 

  4. A. Auerbach: Interacting Electrons and Quantum Magnetism (Springer-Verlag, Berlin Heidelberg New York, 1994)

    Google Scholar 

  5. P. Anderson: Phys. Rev. 86, 694 (1952)

    Article  MATH  ADS  Google Scholar 

  6. J. Chalker, P.C.W. Holdsworth, E.F. Shender: Phys. Rev. Lett. 68, 855 (1992)

    Article  ADS  Google Scholar 

  7. I. Richtey, P. Chandra, P. Coleman: Phys. Rev. B 47, 15342 (1993)

    Article  ADS  Google Scholar 

  8. B. Canals, C. Lacroix: Phys. Rev. Lett. 80, 2933 (1998)

    Article  ADS  Google Scholar 

  9. R. Moessner, J.T. Chalker: Phys. Rev. B 58, 12049 (1998)

    Article  ADS  Google Scholar 

  10. J.-B. Fouet, P. Sindzingre, C. Lhuillier: Eur. Phys. J. B 20, 241 (2001)

    Article  ADS  Google Scholar 

  11. P. Tomczak, J. Richter: Phys. Rev. B 59, 107 (1999)

    Article  ADS  Google Scholar 

  12. N. Trivedi, D. Ceperley: Phys. Rev. B 41, 4552 (1990)

    Article  ADS  Google Scholar 

  13. C. Waldtmann et al.: Eur. Phys. J. B 2, 501 (1998)

    Article  ADS  Google Scholar 

  14. B. Bernu, P. Lecheminant, C. Lhuillier, L. Pierre: Phys. Rev. B 50, 10048 (1994)

    Article  ADS  Google Scholar 

  15. P. Chandra, B. Doucot: Phys. Rev. B 38, 9335 (1988)

    Article  ADS  Google Scholar 

  16. P. Chandra, P. Coleman, A. Larkin: J. Phys. Cond. Matt. 2, 7933 (1990)

    Article  ADS  Google Scholar 

  17. H. Schultz, T. Ziman: Europhys. Lett. 8, 355 (1992)

    Article  ADS  Google Scholar 

  18. J. Villain, R. Bidaux, J. Carton, R. Conte: J. Phys. Fr. 41, 1263 (1980)

    Article  MathSciNet  Google Scholar 

  19. E.F. Shender: Sov. Phys. J.E.T.P. 56, 178 (1982)

    Google Scholar 

  20. C.K. Majumdar, D.K. Ghosh: J. of Math. Phys. 10, 1388 (1969)

    Article  ADS  MathSciNet  Google Scholar 

  21. B. Shastry, B. Sutherland: Phys. Rev. Lett. 47, 964 (1981)

    Article  ADS  Google Scholar 

  22. H. Yokoyama, Y. Saiga: J. Phys. Soc. Jpn. 66, 3617 (1997)

    Article  ADS  Google Scholar 

  23. M.E. Zhitomirsky, K. Ueda: Phys. Rev. B 54, 9007 (1996)

    Article  ADS  Google Scholar 

  24. L. Capriotti, S. Sorella: Phys. Rev. Lett. 84, 3173 (2000)

    Article  ADS  Google Scholar 

  25. N. Read, S. Sachdev: Phys. Rev. B 42, 4568 (1990)

    Article  ADS  Google Scholar 

  26. R. Moessner, S.L. Sondhi, P. Chandra: Phys. Rev. B 64, 144416 (2001)

    Article  ADS  Google Scholar 

  27. D. Rokhsar, S. Kivelson: Phys. Rev. Lett. 61, 2376 (1988)

    Article  ADS  Google Scholar 

  28. M.E. Fisher, J. Stephenson: Phys. Rev. 132, 1411 (1963)

    Article  MATH  ADS  MathSciNet  Google Scholar 

  29. V.N. Kotov, J. Oitmaa, O. Sushkov, Z. Weihong: Phys. Rev. 60, 14613 (1999)

    Article  Google Scholar 

  30. J.-B. Fouet, M. Mambrini, P. Sindzingre, C. Lhuillier: cond-mat/0108070

    Google Scholar 

  31. I. Affleck, J. Marston: Phys. Rev. B 37, 3774 (1988)

    Article  ADS  Google Scholar 

  32. D. Arovas, A. Auerbach: Phys. Rev. B 38, 316 (1988)

    Article  ADS  Google Scholar 

  33. I. Affleck, T. Kennedy, E. Lieb, H. Tasaki: Phys. Rev. Lett. 59, 799 (1987)

    Article  ADS  Google Scholar 

  34. N. Read, S. Sachdev: Phys. Rev. Lett. 66, 1773 (1991)

    Article  ADS  Google Scholar 

  35. N. Katoh, M. Imada: J. Phys. Soc. Jpn. 63, 4529 (1994)

    Article  ADS  Google Scholar 

  36. M. Troyer, H. Tsnunetsgu, D. Wurte: Phys. Rev. B 50, 13515 (1994)

    Article  ADS  Google Scholar 

  37. S. Taniguchi et al.: J. Phys. Soc. Jpn. 64, 2758 (1995)

    Article  ADS  Google Scholar 

  38. Y. Fukumoto, A. Oguchi: J. Phys. Soc. Jpn. 65, 1440 (1996)

    Article  ADS  Google Scholar 

  39. M. Albrecht, F. Mila: Europhys. Lett 34, 145 (1996)

    Article  ADS  Google Scholar 

  40. M. Albrecht, F. Mila: Phys. Rev. B 53, 2945 (1996)

    Article  ADS  Google Scholar 

  41. T. Miyasaki, D. Yoshioka: J. Phys. Soc. Jpn. 65, 2370 (1996)

    Article  ADS  Google Scholar 

  42. S. Sachdev, N. Read: Phys. Rev. Lett. 77, 4800 (1996)

    Article  ADS  Google Scholar 

  43. K. Ueda, H. Kontani, M. Sigrist, P.A. Lee: Phys. Rev. Lett. 76, 1932 (1996)

    Article  ADS  Google Scholar 

  44. K. Kodama et al.: J. Phys. Soc. Jpn. 65, 1941 (1996)

    Article  ADS  Google Scholar 

  45. M. Troyer, H. Kontani, K. Ueda: Phys. Rev. Lett. 76, 3822 (1996)

    Article  ADS  Google Scholar 

  46. K. Kodama et al.: J. Phys. Soc. Jpn. 66, 28 (1997)

    Article  Google Scholar 

  47. T. Ohama, H. Yasuoka, M. Isobe, Y. Ueda: J. Phys. Soc. Jpn. 66, 23 (1997)

    Article  ADS  Google Scholar 

  48. B. Shastry, B. Sutherland: Physica B (Amsterdam) 108, 1069 (1981)

    Article  Google Scholar 

  49. H. Kageyama et al.: Phys. Rev. Lett. 82, 3168 (1999)

    Article  ADS  Google Scholar 

  50. P. Anderson: Mater. Res. Bull. 8, 153 (1973)

    Article  Google Scholar 

  51. S. Liang, B. Doucot, P. Anderson: Phys. Rev. Lett. 61, 365 (1988)

    Article  ADS  Google Scholar 

  52. B. Sutherland: Phys. Rev. B 37, 3786 (1988)

    Article  ADS  Google Scholar 

  53. N. Read, B. Chakraborty: Phys. Rev. B 40, 7133 (1989)

    Article  ADS  Google Scholar 

  54. X. Wen: Phys. Rev. B 44, 2664 (1991)

    Article  ADS  Google Scholar 

  55. G. Misguich, C. Lhuillier, B. Bernu, C. Waldtmann: Phys. Rev. B 60, 1064 (1999)

    Article  ADS  Google Scholar 

  56. M. Oshikawa: Phys. Rev. Lett. 84, 1535 (2000)

    Article  ADS  Google Scholar 

  57. G. Misguich, C. Lhuillier, M. Mambrini, P. Sindzingre: cond-mat/0112360 (to appear in Eur. Phys. J. B)

    Google Scholar 

  58. R. Moessner, S.L. Sondhi: Phys. Rev. Lett. 86, 1881 (2001)

    Article  ADS  Google Scholar 

  59. R. Coldea, D.A. Tennant, A.M. Tsvelick, Z. Tylczynski: Phys. Rev. Lett. 86, 1335 (2001)

    Article  ADS  Google Scholar 

  60. C. Nayak, K. Shtengel: Phys. Rev. B 64, 064422 (2001)

    Article  ADS  Google Scholar 

  61. C.H. Chung, J.B. Marston, S. Sachdev: Phys. Rev. B 64, 134407 (2001)

    Article  ADS  Google Scholar 

  62. C.H. Chung, J.B. Marston, R.H. McKenzie: J. Phys.: Condens. Matter 13, 5159 (2001)

    Article  ADS  Google Scholar 

  63. P. Anderson: Science 235, 1196 (1987)

    Article  ADS  Google Scholar 

  64. R. Moessner, S.L. Sondhi, P. Chandra: Phys. Rev. Lett. 84, 4457 (2000)

    Article  ADS  Google Scholar 

  65. R. Moessner, S.L. Sondhi, E. Fradkin: Phys.Rev. B 65, 024504 (2002)

    Article  ADS  Google Scholar 

  66. A. Parola, S. Sorella, Q. Zhong: Phys. Rev. Lett. 71, 4393 (1993)

    Article  ADS  Google Scholar 

  67. G. Santoro et al.: Phys. Rev. Lett. 83, 3065 (1999)

    Article  ADS  Google Scholar 

  68. D. Thouless: Proc. Phys. Soc. 86, 893 (1965)

    Article  MathSciNet  ADS  Google Scholar 

  69. M. Roger, J. Hetherington, J. Delrieu: Rev. Mod. Phys. 55, 1 (1983)

    Article  ADS  Google Scholar 

  70. C. Herring: in Magnetism vol. IV, G.T. Rado, H. Suhl eds. (Academic press, New York and London, 1966)

    Google Scholar 

  71. M. Roger et al.: Phys. Rev. Lett. 80, 1308 (1998)

    Article  ADS  Google Scholar 

  72. G. Misguich, B. Bernu, C. Lhuillier, C. Waldtmann: Phys. Rev. Lett. 81, 1098 (1998)

    Article  ADS  Google Scholar 

  73. E. Collin et al.: Phys. Rev. Lett. 86, 2447 (2001)

    Article  ADS  Google Scholar 

  74. B. Bernu, L. Candido, D. Ceperley: Phys. Rev. Lett. 86, 870 (2001)

    Article  ADS  Google Scholar 

  75. L. Regnault, J. Rossat-Mignod: in Phase transitions in quasi two-dimensional planar magnets, ed. L.J.D. Jongh (Kluwer Academic Publishers, The Netherlands, 1990), pp. 271–320

    Google Scholar 

  76. X. Wen, F. Wilczek, A. Zee: Phys. Rev. B 39, 11413 (1989)

    Article  ADS  Google Scholar 

  77. V. Kalmeyer, R. Laughlin: Phys. Rev. Lett. 59, 2095 (1987)

    Article  ADS  Google Scholar 

  78. V. Kalmeyer, R. Laughlin: Phys. Rev. B 39, 11879 (1989)

    Article  ADS  Google Scholar 

  79. K. Yang, L. Warman, S. Girvin: Phys. Rev. Lett. 70, 2641 (1993)

    Article  ADS  Google Scholar 

  80. W. LiMing, G. Misguich, P. Sindzingre, C. Lhuillier: Phys. Rev. B 62, 6372 (2000)

    Article  ADS  Google Scholar 

  81. M. Mambrini, F. Mila: Eur. Phys. J. B 17, 651,659 (2001)

    Article  ADS  Google Scholar 

  82. C. Zeng, V. Elser: Phys. Rev. B 42, 8436 (1990)

    Article  ADS  Google Scholar 

  83. F. Mila: Phys. Rev. Lett. 81, 2356 (1998)

    Article  ADS  Google Scholar 

  84. C. Lhuillier, P. Sindzingre, J.-B. Fouet: cond-mat/0009336

    Google Scholar 

  85. P. Lecheminant et al.: Phys. Rev. B 56, 2521 (1997)

    Article  ADS  Google Scholar 

  86. Y. Uemura et al.: Phys. Rev. Lett. 73, 3306 (1994)

    Article  ADS  Google Scholar 

  87. J. Marston, C. Zeng: J. Appl. Phys. 69, 5962 (1991)

    Article  ADS  Google Scholar 

  88. R. Siddharthan, A. Georges: Phys. Rev. B 65, 014417 (2002)

    Article  ADS  Google Scholar 

  89. A. Georges, R. Siddharthan, S. Florens: Phys. Rev. Lett. 87, 277203 (2001)

    Article  ADS  Google Scholar 

  90. N. Wada et al.: J. Phys. Soc. Jpn. 66, 961 (1997)

    Article  ADS  Google Scholar 

  91. A.P. Ramirez: Annu. Rev. Matter. Sci. 24, 453–480, (1994) and references therein.

    Article  ADS  Google Scholar 

  92. S.-H. Lee et al.: Europhys. Lett 35, 127 (1996)

    Article  ADS  Google Scholar 

  93. A.P. Ramirez, B. Hessen, M. Winkelmann: Phys. Rev. Lett. 84, 2957 (2000)

    Article  ADS  Google Scholar 

  94. P. Sindzingre et al.: Phys. Rev. Lett. 84, 2953 (2000)

    Article  ADS  Google Scholar 

  95. A. Keren et al.: Phys. Rev. B 53, 6451 (1996)

    Article  ADS  Google Scholar 

  96. A. Wills et al.: Phys. Rev. B 62, R9264 (2000)

    Article  ADS  Google Scholar 

  97. M.J. Harris et al.: Phys. Rev. Lett. 73, 189 (1994)

    Article  ADS  Google Scholar 

  98. S. Palmer, J. Chalker: condmat/0102447

    Google Scholar 

  99. R. Moessner, O. Tchernyshyov, S.L. Sondhi: cond-mat/0106286

    Google Scholar 

  100. M.E. Zhitomirsky, T. Nikuni: Phys. Rev. B 57, 5013 (1998)

    Article  ADS  Google Scholar 

  101. A. Honecker: cond-mat/0009006

    Google Scholar 

  102. I. Affleck: Phys. Rev. B 43, 3215 (1991)

    Article  ADS  Google Scholar 

  103. K. Kubo, T. Momoi: Z. Phys. B. Condens. Matter 103, 485 (1997)

    Article  ADS  Google Scholar 

  104. T. Momoi, H. Sakamoto, K. Kubo: Phys. Rev. B 59, 9491 (1999)

    Article  ADS  Google Scholar 

  105. G. Misguich: Ph.D. thesis, Université Pierre et Marie Curie. Paris. France, 1999

    Google Scholar 

  106. H. Kawamura, S. Miyashita: J. Phys. Soc. Jpn. 54, 4530 (1985)

    Article  ADS  Google Scholar 

  107. H. Nishimori, S. Miyashita: J. Phys. Soc. Jpn. 55, 4448 (1986)

    Article  ADS  Google Scholar 

  108. A.V. Chubukov, D.I. Golosov: J. Phys.: Condens. Matter 3, 69 (1991)

    Article  ADS  Google Scholar 

  109. A. Honecker: J. Phys. Condens. Matter 11, 4697 (1999)

    Article  ADS  Google Scholar 

  110. E.H. Lieb, T.D. Schultz, D.C. Mattis.: Ann. Phys. (N.Y) 16, 407 (1961)

    Article  MATH  ADS  MathSciNet  Google Scholar 

  111. M. Oshikawa, M. Yamanaka, I. Affleck: Phys. Rev. Lett. 78, 1984 (1997)

    Article  ADS  Google Scholar 

  112. K. Totsuka: Phys. Rev. B 57, 3454 (1998)

    Article  ADS  Google Scholar 

  113. D.C. Cabra, A. Honecker, P. Pujol: Phys. Rev. Lett. 79, 5126 (1997)

    Article  ADS  Google Scholar 

  114. A. Honecker: Phys. Rev. B 59, 6790 (1999)

    Article  ADS  Google Scholar 

  115. A. Honecker, F. Mila, M. Troyer: Eur. Phys. J. B 15, 227 (2000)

    Article  ADS  Google Scholar 

  116. Y. Fukumoto, A. Oguchi: J. Phys. Soc. Jpn. 68, 3655 (1999)

    Article  ADS  Google Scholar 

  117. T. Momoi, K. Totsuka: Phys. Rev. B 61, 3231 (2000)

    Article  ADS  Google Scholar 

  118. E. Müller-Hartmann, R.R.P. Singh, C. Knetter, G.S. Uhrig: Phys. Rev. Lett. 84, 1808 (2000)

    Article  ADS  Google Scholar 

  119. K. Onizuka et al.: J. Phys. Soc. Jpn. 69, 1016 (2000)

    Article  ADS  Google Scholar 

  120. S. Miyahara, K. Ueda: Phys. Rev. Lett. 82, 3701 (1999)

    Article  ADS  Google Scholar 

  121. S. Miyahara, K. Ueda: Phys. Rev. B 61, 3417 (2000)

    Article  ADS  Google Scholar 

  122. H. Kageyama et al.: Phys. Rev. Lett. 84, 5876 (2000)

    Article  ADS  Google Scholar 

  123. T. Momoi, K. Totsuka: Phys. Rev. B 62, 15067 (2000)

    Article  ADS  Google Scholar 

  124. G. Misguich, T. Jolicoeur, S.M. Girvin: Phys. Rev. Lett. 87, 097203 (2001)

    Article  ADS  Google Scholar 

  125. E. Fradkin: Phys. Rev. Lett. 63, 322 (1989)

    Article  ADS  MathSciNet  Google Scholar 

  126. D. Eliezer, G.W. Semenoff: Ann. Phys. (New York) 217, 66 (1992)

    Article  MATH  ADS  MathSciNet  Google Scholar 

  127. A. Lopez, A.G. Rojo, E. Fradkin: Phys. Rev. B 49, 15139 (1994)

    Article  ADS  Google Scholar 

  128. D.R. Hofstadter: Phys. Rev. B 14, 2239 (1976)

    Article  ADS  Google Scholar 

  129. S.C. Zhang: Int. J. Mod. Phys B 6, 25 (1992)

    Article  ADS  Google Scholar 

  130. F. Haldane, D.P. Arovas: Phys. Rev. B 52, 4223 (1995)

    Article  ADS  Google Scholar 

  131. D. Thouless, M. Kohmoto, M.P. Nightingale, M. den Nijs: Phys. Rev. Lett. 49, 405 (1982)

    Article  ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Laboratoire de Physique Théorique des Liquides, Université P. et M. Curie and UMR 7600 of CNRS, case 121, 4 Place Jussieu, 75252, Paris Cedex

    Claire Lhuillier

  2. Service de Physique Théorique, CEA Saclay, F-91191, Gif-sur-Yvette Cedex

    Grégoire Misguich

Authors
  1. Claire Lhuillier
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Grégoire Misguich
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Grenoble High Magnetic Field Laboratory, BP 166, 38042, Grenoble Cedex 9, France

    C. Berthier , L. P. Lévy  & G. Martinez ,  & 

Rights and permissions

Reprints and permissions

Copyright information

© 2002 Springer-Verlag Berlin Heidelberg

About this chapter

Cite this chapter

Lhuillier, C., Misguich, G. (2002). Frustrated Quantum Magnets. In: Berthier, C., Lévy, L.P., Martinez, G. (eds) High Magnetic Fields. Lecture Notes in Physics, vol 595. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45649-X_6

Download citation

  • DOI: https://doi.org/10.1007/3-540-45649-X_6

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-43979-0

  • Online ISBN: 978-3-540-45649-0

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation