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Quantum magnetism in two dimensions: From semi-classical Néel order to magnetic disorder

  • Johannes Richter
  • Jörg Schulenburg
  • Andreas Honecker
Chapter
Part of the Lecture Notes in Physics book series (LNP, volume 645)

Abstract

It is known from the Mermin-Wagner theorem that magnetic long-range order can exist in two dimensions only at zero temperature, but even then it can still be destroyed e.g. by quantum fluctuations or geometric frustration. In this context, we review ground-state features of the s=1/2 Heisenberg antiferromagnet on two-dimensional lattices. In order to discuss the interplay of lattice topology and quantum fluctuations we focus on the 11 two-dimensional uniform Archimedean lattices which include e.g. the square, triangular and kagomé lattice. The ground state of the spin-1/2 Heisenberg antiferromagnet is likely to be semi-classically ordered in most cases. However, the interplay of geometric frustration and quantum fluctuations gives rise to a quantum paramagnetic ground state without semi-classical long-range order on two lattices which are precisely those among the 11 uniform Archimedean with a highly degenerate ground state in the classical limit s→∞. The first one is the famous kagomé lattice where many low-lying singlet excitations are known to arise in the spin gap. The second lattice, called star lattice, is a new example for a quantum paramagnet and has a clear gap to all excitations.

Modification of certain bonds leads to quantum phase transitions which are also discussed briefly. Furthermore, we discuss the magnetization process of the Heisenberg antiferromagnet on the 11 Archimedean lattices, focusing on anomalies like plateaus and a magnetization jump just below the saturation field. As an illustration we discuss the two-dimensional Shastry-Sutherland model which is used to describe SrCu2(BO3)2.

Keywords

Magnetization Curve Triangular Lattice Quantum Phase Transition Quantum Magnetism Exact Diagonalization 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1.
    T. Barnes: Int. J. Mod. Phys. C 2 659 (1991).ADSCrossRefGoogle Scholar
  2. 2.
    E. Manousakis: Rev. Mod. Phys. 63, 1 (1991).ADSCrossRefGoogle Scholar
  3. 3.
    E. Dagotto: Rev. Mod. Phys. 66, 763 (1994).ADSCrossRefGoogle Scholar
  4. 4.
    S. Taniguchi, T. Nishikawa, Y. Yasui, Y. Kobayashi, M. Sato, T. Nishioka, M. Kontani, K. Sano: J. Phys. Soc. Jpn. 64, 2758 (1995).ADSCrossRefGoogle Scholar
  5. 5.
    H. Kageyama, K. Yoshimura, R. Stern, N.V. Mushnikov, K. Onizuka, M. Kato, K. Kosuge, C.P. Slichter, T. Goto, Y. Ueda: Phys. Rev. Lett. 82, 3168 (1999)ADSCrossRefGoogle Scholar
  6. 6.
    H. Tanaka, T. Ono, H. Aruga Katori, H. Mitamura, F. Ishikawa, T. Goto: Progr. Theor. Phys. Suppl. 145, 101 (2002)ADSCrossRefGoogle Scholar
  7. 7.
    N.D. Mermin, H. Wagner: Phys. Rev. Lett. 17, 1133 (1966)ADSCrossRefGoogle Scholar
  8. 8.
    P.W. Anderson: Mater. Res. Bull. 8, 153 (1973)CrossRefGoogle Scholar
  9. 9.
    P. Fazekas, P.W. Anderson: Philos. Mag. 30, 123 (1974)CrossRefGoogle Scholar
  10. 10.
    S. Sachdev: Quantum Phase Transitions (Cambridge University Press, Cambridge 1999)zbMATHGoogle Scholar
  11. 11.
    C. Lhuillier, P. Sindzingre, J.-B. Fouet: Can. J. Phys. 79, 1525 (2001)ADSCrossRefGoogle Scholar
  12. 12.
    C. Lhuillier, G. Misguich: Frustrated quantum magnets In: High magnetic fields, ed by C. Berthier, L.P. Lévy, G. Martinez, Lecture Notes in Physics 595 (Springer, Berlin, 2001) pp 161–190.CrossRefGoogle Scholar
  13. 13.
    P. Sindzingre, C. Lhuillier, J.-B. Fouet: Quantum phases in two-dimensional frustrated spin-1/2-antiferromgnets In: Series on Advances in Quantum Many-Body Theory. vol. 6 ed by R.F. Bishop, T. Brandes, K.A. Gernoth, N.R. Walet, Y. Xian (World Scientific, Singapore 2002) pp 90–98Google Scholar
  14. 14.
    C. Lhuillier, P. Sindzingre: Spin-1/2 antiferromagnets in 2 dimensions In: Quantum Properties of Low-Dimensional Antiferromagnets, ed by Y. Ajiro, J.-P. Boucher (Kyushu University Press 2002) pp 111–117 (also: cond-mat/0212351)Google Scholar
  15. 15.
    G. Misguich, C. Lhuillier: Two-dimensional quantum antiferromagnets. cond-mat/0310405. 2003.Google Scholar
  16. 16.
    B. Canals, C. Lacroix: Phys. Rev. Lett. 80, 2933 (1998)ADSCrossRefGoogle Scholar
  17. 17.
    Spinpack homepage: http://www-e.uni-magdeburg.de/jschulen/spin/Google Scholar
  18. 18.
    J. Schuleuburg: Einfluß der Gitterstruktur auf den Grundzustand von s=1/2-Quantenspinsystemen. PhD thesis, University of Magdeburg (2002) [http://www-e.uni-magdeburg.de/jschulen/diss.html]Google Scholar
  19. 19.
    S. Chakravartry, B.I. Halperin, D.R. Nelson: Phys. Rev. B 39, 2344 (1989)ADSCrossRefGoogle Scholar
  20. 20.
    A.V. Chubukov, S. Sachdev, T. Senthil: Nuclear Phys. B 426, 601 (1994)ADSCrossRefGoogle Scholar
  21. 21.
    J. Richter, S. Krüger, D. Farnell, R. Bishop: Quantum phase transitions in spin systems In: Series on Advances in Quantum Many-Body Theory. vol. 5 ed by R.F. Bishop. K.A. Gernoth, N.R. Walet (World Scientific, Singapore 2001) pp 239–246CrossRefGoogle Scholar
  22. 22.
    F. Mila: Quantum Frustrated Magnets: From Theory to Experiment In: Series on Advances in Quantum Many Body Theory. vol. 6 ed by R.F. Bishop, T. Brandes, K.A. Gernoth, N.R. Walet, Y. Xian (World Scientific, Singapore 2002) pp 80–89Google Scholar
  23. 23.
    B. Grünbaum, G.C. Shephard: Tilings and Patterns. W.H. Freeman and Company, New York (1987)zbMATHGoogle Scholar
  24. 24.
    P.N. Suding, R.M. Ziff: Phys. Rev. E 60, 275 (1999).ADSCrossRefGoogle Scholar
  25. 25.
    S. Kobe, K. Handrich: Phys. Stat. Sol. b 73, K65 (1976); J. Richter, S. Kobe: J. Phys. C 15, 2193 (1982); S. Kobe, T. Klotz: Phys. Rev. E 52, 5660 (1995)ADSCrossRefGoogle Scholar
  26. 26.
    R.R.P. Singh, M.P. Gelfand, D.A. Huse: Phys. Rev. Lett. 61, 2484 (1988)ADSCrossRefGoogle Scholar
  27. 27.
    S.E. Krüger, J. Richter, J. Schulenburg, D.J.J. Farnell, R.F. Bishop: Phys. Rev. B 61, 14607 (2000); S.E. Krüger, J. Richter: Phys. Rev. B 64, 024433 (2001)ADSCrossRefGoogle Scholar
  28. 28.
    W. Marshall: Proc. Roy. Soc. A 232, 48 (1955)ADSCrossRefGoogle Scholar
  29. 29.
    E. Lieb, D. Mattis: J. Math. Phys. 3, 749 (1962)ADSCrossRefGoogle Scholar
  30. 30.
    J. Richter, N.B. Ivanov, K. Retzlaff, A. Voigt: J. Magn. Magn. Mat. 140–144, 1611 (1995)CrossRefGoogle Scholar
  31. 31.
    B. Bernu, C. Lhuillier, L. Pierre: Phys. Rev. Lett. 69, 2590 (1992)ADSCrossRefGoogle Scholar
  32. 32.
    D.D. Betts, J. Schulenburg, G.E. Stewart, J. Richter, J.S. Flynn: J. Phys. A: Math. Gen. 31, 7685 (1998)ADSCrossRefGoogle Scholar
  33. 33.
    D.D. Betts, H.Q. Lin, J.S. Flynn: Can. J. Phys. 77, 353 (1999)ADSCrossRefGoogle Scholar
  34. 34.
    P.W. Anderson: Phys. Rev. 86, 694 (1952)ADSCrossRefGoogle Scholar
  35. 35.
    H. Neuberger, T. Ziman: Phys. Rev. B 39, 2608 (1989)ADSCrossRefGoogle Scholar
  36. 36.
    B. Bernu, P. Lecheminant, C. Lhuillier, L. Pierre: Physica Scripta T 49, 192 (1993)ADSCrossRefGoogle Scholar
  37. 37.
    B. Bernu, P. Lecheminant, C. Lhuillier, L. Pierre: Phys. Rev. B 50, 10048 (1994)ADSCrossRefGoogle Scholar
  38. 38.
    P. Lecheminant, B. Bernu, C. Lhuillier, L. Pierre, P. Sindzingre: Phys. Rev. B 56, 2521 (1997)ADSCrossRefGoogle Scholar
  39. 39.
    Ch. Wakltmann, H.-U. Everts, B. Bernu, C. Lhuillier, P. Sindzingre, P. Lecheminant, L. Pierre: Eur. Phys. J. B 2, 501 (1998)ADSCrossRefGoogle Scholar
  40. 40.
    J. Richter, N.B. Ivanov, K. Retzlaff: acta physica slovaca 44, 365 (1994)Google Scholar
  41. 41.
    A. Voigt, J. Richter, P. Tomczak: Physica A 299, 461 (2001)ADSCrossRefGoogle Scholar
  42. 42.
    J.B. Fouet, P. Sindzingre, C. Lhuillier: Eur. Phys. J. B 20, 241 (2001)ADSCrossRefGoogle Scholar
  43. 43.
    P. Tomczak, J. Schulenburg, J. Richter, A.R. Ferchmin: J. Phys.: Condens. Matter 13, 3851 (2001)ADSGoogle Scholar
  44. 44.
    P. Hasenfratz, H. Leutwyler: Nuclear Phys. B 343, 241 (1990)ADSCrossRefGoogle Scholar
  45. 45.
    P. Hasenfratz, F. Niedermayer: Z. Phys. B 92, 91 (1993)ADSCrossRefGoogle Scholar
  46. 46.
    J. Oitmaa, C.J. Hamer, Zheng Weihong: Phys. Rev. B 50, 3877 (1994)ADSCrossRefGoogle Scholar
  47. 47.
    A.W. Sandvik: Phys. Rev. B 56, 11678 (1997)ADSCrossRefGoogle Scholar
  48. 48.
    M. Troyer, H. Kontani, K. Ueda: Phys. Rev. Lett. 76, 3822 (1996)ADSCrossRefGoogle Scholar
  49. 49.
    E.J. Neves, J.F. Perez: Phys. Lett., 114A, 331 (1986)ADSCrossRefGoogle Scholar
  50. 50.
    I. Affleck, T. Kennedy, E.H. Lieb, H. Tasaki: Commun. Math. Phys. 115, 477 (1988)ADSMathSciNetCrossRefGoogle Scholar
  51. 51.
    K. Kubo, T. Kishi: Phys. Rev. Lett. 61, 2585 (1988)ADSCrossRefGoogle Scholar
  52. 52.
    H.-A. Wischmann, E. Müller-Hartmann: J. Phys. I (Paris) 1, 647 (1991)Google Scholar
  53. 53.
    M. Greven, R.J. Birgeneau, Y. Endoh, M.A. Kastner, B. Keimer, M. Matsuda, G. Shirane, T.R. Thurston: Phys. Rev. Lett. 72, 1096 (1994)ADSCrossRefGoogle Scholar
  54. 54.
    F.M. Woodward, A.S. Albrecht, C.M. Wynn, C.P. Landee, M.M. Turnbull: Phys. Rev. B 65, 144412 (2002)ADSCrossRefGoogle Scholar
  55. 55.
    H.J. Schulz, T.A.L. Ziman: Europhys. Lett. 18, 355 (1992); H.J. Schulz, T.A.L. Ziman, D. Poilblanc: J. Phys. I France 6, 675 (1996)ADSCrossRefGoogle Scholar
  56. 56.
    Zheng Weihong, C.J. Hamer: Phys. Rev. B 47, 7961 (1993)ADSCrossRefGoogle Scholar
  57. 57.
    R.F. Bishop, D.J.J. Farnell, S.E. Krüger, J.B. Parkinson, J. Richter: J. Phys. Condens. Matter 12, 6887 (2000)ADSCrossRefGoogle Scholar
  58. 58.
    Zheng Weihong, J. Oitmaa, C.J. Hamer: Phys. Rev. B 43, 8321 (1991)ADSCrossRefGoogle Scholar
  59. 59.
    J.D. Reger, J.A. Riera, A. P. Young: J. Phys.: Condens. Matter 1, 1855 (1989)ADSGoogle Scholar
  60. 60.
    Zheng Weihong, J. Oitmaa, C.J. Hamer: Phys. Rev. B 44, 11869 (1991)ADSCrossRefGoogle Scholar
  61. 61.
    J. Oitmaa, C.J. Hamer, Zheng Weihong: Phys. Rev. B 45, 9834 (1992)ADSCrossRefGoogle Scholar
  62. 62.
    A. Mattsson, P. Fröjdh, T. Einarsson: Phys. Rev. B 49, 3997 (1994)ADSCrossRefGoogle Scholar
  63. 63.
    N. Katoh, M. Imada: J. Phys. Soc. Jpn. 64, 4105 (1995)ADSCrossRefGoogle Scholar
  64. 64.
    K. Ueda, H. Kontani, M. Sigrist, P.A. Lee: Phys. Rev. Lett. 76, 1932 (1996).ADSCrossRefGoogle Scholar
  65. 65.
    O.A. Starykh, M.E. Zhitomirsky, D.I. Khomskii, R.R.P. Singh K. Ueda: Phys. Rev. Lett. 77, 2558 (1996)ADSCrossRefGoogle Scholar
  66. 66.
    M.P. Gelfand, Zheng Weihong, R.R.P. Singh, J. Oitmaa, C.J. Hamer: Phys. Rev. Lett. 77, 2794 (1996)ADSCrossRefGoogle Scholar
  67. 67.
    M. Albrecht, F. Mila: Phys. Rev. B 53, R2945 (1996)ADSCrossRefGoogle Scholar
  68. 68.
    M. Albrecht, F. Mila, D. Poilblanc: Phys. Rev. B 54, 15856 (1996)ADSCrossRefGoogle Scholar
  69. 69.
    Zheng Weihong, M.P. Gelfand, R.R.P. Singh, J. Oitmaa, C.J. Hamer: Phys. Rev. B 55, 11377 (1997)ADSCrossRefGoogle Scholar
  70. 70.
    M. Troyer, M. Imada, K. Ueda: J. Phys. Soc. Jpn. 66, 2957 (1997)ADSCrossRefGoogle Scholar
  71. 71.
    I. Bose, A. Ghosh: Phys. Rev. B 56,3149 (1997)ADSCrossRefGoogle Scholar
  72. 72.
    L.O. Manuel, M.I. Micheletti, A.E. Trumper, H.A. Ceccatto: Phys. Rev. B 58, 8490 (1998)ADSCrossRefGoogle Scholar
  73. 73.
    Zheng Weihong, J. Oitmaa, C.J. Hamer: Phys. Rev. B 58, 14147 (1998)ADSCrossRefGoogle Scholar
  74. 74.
    J. Richter, N.B. Ivanov, J. Schulenburg: J. Phys.: Condens. Matter 10, 3635 (1998)ADSGoogle Scholar
  75. 75.
    M.A. Korotin, I.S. Elfimov, V.I. Anisimov, M. Troyer, D.I. Khomskii: Phys. Rev. Lett. 83, 1387 (1999)ADSCrossRefGoogle Scholar
  76. 76.
    C.S. Hellberg, W.E. Pickett, L.L. Boyer, H.T. Stokes, M.J. Mehl: J. Phys. Soc. Jpn. 68, 3489 (1999)ADSCrossRefGoogle Scholar
  77. 77.
    Y. Fukumoto, A. Oguchi: J. Phys. Soc. Jpn. 68, 3655 (1999)ADSCrossRefGoogle Scholar
  78. 78.
    P. Tomczak, J. Richter: Phys. Rev. B 59, 107 (1999)ADSCrossRefGoogle Scholar
  79. 79.
    D.A. Huse, V. Elser: Phys. Rev. Lett. 60, 2531 (1988)ADSCrossRefGoogle Scholar
  80. 80.
    Th. Jolicoeur, J.C. Le Guillon: Phys. Rev. B 40, 2727R (1989)ADSCrossRefGoogle Scholar
  81. 81.
    S.J. Miyake: J. Phys. Soc. Jpn. 61, 983 (1992)ADSCrossRefGoogle Scholar
  82. 82.
    R. Deutscher, H.U. Everts: Z. Phys. B 93, 77 (1993)ADSCrossRefGoogle Scholar
  83. 83.
    A.E. Trumper: Phys. Rev. B 60, 2987 (1999)ADSCrossRefGoogle Scholar
  84. 84.
    L. Capriotti, A.E. Trumper, S. Sorella: Phys. Rev. Lett. 82, 3899 (1999)ADSCrossRefGoogle Scholar
  85. 85.
    L. Capriotti: Int. J. of Mod. Phys. B 15, 1799 (2001)ADSCrossRefGoogle Scholar
  86. 86.
    D.J.J. Farnell, R.F. Bishop, K.A. Gernoth: Phys. Rev. B 63, 220402(R) (2001)ADSCrossRefGoogle Scholar
  87. 87.
    S. Miyashita: J. Phys. Soc. Jpn. 55, 3605 (1986)ADSCrossRefGoogle Scholar
  88. 88.
    A. Honecker: J. Phys.: Condens. Matter 11, 4697 (1999)ADSGoogle Scholar
  89. 89.
    D.D. Betts: Proc. N.S. Inst. Sci. 40, 95 (1995)Google Scholar
  90. 90.
    D. Schmalfuß, P. Tomczak, J. Schulenburg, J. Richter: Phys. Rev. B 65, 224405 (2002)ADSCrossRefGoogle Scholar
  91. 91.
    B. Normand, K. Penc, M. Albrecht, F. Mila: Phys. Rev. B 56, R5736 (1997)ADSCrossRefGoogle Scholar
  92. 92.
    S. Miyahara, M. Troyer, D.C. Johnston, K. Ueda: J. Phys. Soc. Jpn. 67, 3918 (1998)ADSCrossRefGoogle Scholar
  93. 93.
    B.S. Shastry, B. Sutherland: Physica B 108, 1069 (1981)CrossRefGoogle Scholar
  94. 94.
    M. Albrecht, F. Mila: Europhys. Lett. 34, 145 (1996)ADSCrossRefGoogle Scholar
  95. 95.
    S. Miyahara, K. Ueda: Phys. Rev. Lett. 82, 3701 (1999)ADSCrossRefGoogle Scholar
  96. 96.
    Zheng Weihong, C.J. Hamer, J. Oitmaa: Phys. Rev. B 60, 6608 (1999)ADSCrossRefGoogle Scholar
  97. 97.
    E. Müller-Hartmann, R.R.P. Singh, C. Knetter, G.S. Uhrig: Phys. Rev. Lett. 84, 1808 (2000)ADSCrossRefGoogle Scholar
  98. 98.
    T. Momoi, K. Totsuka: Phys. Rev. B 61, 3231 (2000)ADSCrossRefGoogle Scholar
  99. 99.
    A. Koga, N. Kawakami: Phys. Rev. Lett. 84, 4461 (2000)ADSCrossRefGoogle Scholar
  100. 100.
    G. Misgnich, Th. Jolicocur, S.M. Girvin: Phys. Rev. Lett. 87, 097203 (2001)ADSCrossRefGoogle Scholar
  101. 101.
    C.H. Chung, J.B. Marston, S. Sachdev: Phys. Rev. B 64, 134407 (2001).ADSCrossRefGoogle Scholar
  102. 102.
    Weihong Zheng, J. Oitmaa, C.J. Hamer: Phys. Rev. B 65, 014408 (2001)ADSCrossRefGoogle Scholar
  103. 103.
    D. Carpentier, L. Balents: Phys. Rev. B 65, 024427 (2002)ADSCrossRefGoogle Scholar
  104. 104.
    A. Läuchli, S. Wessel, M. Sigrist: Phys. Rev. B 66, 014401 (2002)ADSCrossRefGoogle Scholar
  105. 105.
    S. Miyahara, K. Ueda: J. Phys.: Condens. Matter 15, R327 (2003)ADSCrossRefGoogle Scholar
  106. 106.
    J. Richter, D.J.J. Farnell: unpublishedGoogle Scholar
  107. 107.
    M. Mekata: Phys. Today 56, 12 (2003).CrossRefGoogle Scholar
  108. 108.
    C. Zeng, V. Elser: Phys. Rev. B 42, 8436 (1990)ADSCrossRefGoogle Scholar
  109. 109.
    A.B. Harris, C. Kallin, A.J. Berlinsky: Phys. Rev. B 45, 2899 (1992)ADSCrossRefGoogle Scholar
  110. 110.
    A. Chubukov: Phys. Rev. Lett. 69, 832 (1992)ADSCrossRefGoogle Scholar
  111. 111.
    P.W. Leung, V. Elser: Phys. Rev. B 47, 5459 (1993)ADSCrossRefGoogle Scholar
  112. 112.
    K. Yang, L.K. Warman, S.M. Girvin: Phys. Rev. Lett. 70, 2641 (1993)ADSCrossRefGoogle Scholar
  113. 113.
    F. Mila: Phys. Rev. Lett. 81, 2356 (1998)ADSCrossRefGoogle Scholar
  114. 114.
    Ch. Waldtmann, H. Kreutzmann, U. Schollwöck, K. Maisinger, H.-U. Everts: Phys. Rev. B 62, 9472 (2000)ADSCrossRefGoogle Scholar
  115. 115.
    Weiqiang Yu, Shiping Feng: Eur. Phys. J. B 13, 265 (2000)ADSCrossRefGoogle Scholar
  116. 116.
    M. Mambrini, F. Mila: Eur. Phys. J. B 17, 651 (2000)ADSCrossRefGoogle Scholar
  117. 117.
    R. Shankar, D. Shubashree: Phys. Rev. B 61, 12126 (2000)ADSCrossRefGoogle Scholar
  118. 118.
    P. Sindzingre, G. Misguich, C. Lhuillier, B. Bernu, L. Pierre, Ch. Waldtmann, H.-U. Everts: Phys. Rev. Lett. 84, 2953 (2000)ADSCrossRefGoogle Scholar
  119. 119.
    A.V. Syromyatnikov, S.V. Maleyev: Phys. Rev. B 66, 132408 (2002)ADSCrossRefGoogle Scholar
  120. 120.
    B.H. Bernhard, B. Canals, C. Lacroix: Phys. Rev. B 66, 104424 (2002)ADSCrossRefGoogle Scholar
  121. 121.
    A.P. Ramirez: Annu. Rev. Mater. Sci. 24, 453 (1994)ADSCrossRefGoogle Scholar
  122. 122.
    A.P. Ramirez, B. Hessen, M. Winkelmann: Phys. Rev. Lett. 84, 2957 (2000)ADSCrossRefGoogle Scholar
  123. 123.
    Z. Hiroi, M. Hanawa, N. Kobayashi, M. Nohara, H. Takagi, Y. Kato, M. Takigawa: J. Phys. Soc. Jpn. 70, 3377 (2001)ADSCrossRefGoogle Scholar
  124. 124.
    C. Gros, P. Lemmens, K.-Y. Choi, G. Güntherodt, M. Baenitz, H.H. Otto: Europhys. Lett. 60, 276 (2002)ADSCrossRefGoogle Scholar
  125. 125.
    J.T. Chalker, P.C.W. Holdsworth, E.F. Shender: Phys. Rev. Lett. 68, 855 (1992)ADSCrossRefGoogle Scholar
  126. 126.
    D.A. Huse, A.D. Rutenberg: Phys. Rev. B 45, 7536 (1992)ADSCrossRefGoogle Scholar
  127. 127.
    J.N. Reimers, A.J. Berlinsky: Phys. Rev. B 48, 9539 (1993)ADSCrossRefGoogle Scholar
  128. 128.
    J.-B. Fouet, M. Mambrini, P. Sindzingre, C. Lhuillier: Phys. Rev. B 67, 054411 (2003)ADSCrossRefGoogle Scholar
  129. 129.
    W. Brenig, A. Honecker: Phys. Rev. B 65, 140407(R) (2002)ADSCrossRefGoogle Scholar
  130. 130.
    W. LiMing, G. Misguich, P. Sindzingre, C. Lhuillier: Phys. Rev. B 62, 6372 (2000)ADSCrossRefGoogle Scholar
  131. 131.
    V.N. Kotov, J. Oitmaa, O. Sushkov, Z. Weihong: Phil. Mag. B 80, 1483 (2000)ADSCrossRefGoogle Scholar
  132. 132.
    P. Chandra, B. Doucot: Phys. Rev. B 38, 9335 (1988)ADSCrossRefGoogle Scholar
  133. 133.
    J. Richter: Phys. Rev. B 47, 5794 (1993)ADSCrossRefGoogle Scholar
  134. 134.
    A.V. Dotsenko, O.P. Sushkov: Phys. Rev. B 50, 13821 (1994)ADSCrossRefGoogle Scholar
  135. 135.
    J. Oitmaa, Zheng Weihong: Phys. Rev. B 54, 3022 (1996)ADSCrossRefGoogle Scholar
  136. 136.
    R.F. Bishop, D.J.J. Farnell, J.B. Parkinson: Phys. Rev. B 58, 6394 (1998)ADSCrossRefGoogle Scholar
  137. 137.
    L. Capriotti, S. Sorella: Phys. Rev. Lett. 84, 3173 (2000)ADSCrossRefGoogle Scholar
  138. 138.
    O.P. Sushkov, J. Oitmaa, Zheng Weihong: Phys. Rev. B 63, 104420 (2001)ADSCrossRefGoogle Scholar
  139. 139.
    Y. Xian: Phys. Rev. B 52, 12485 (1995)ADSCrossRefGoogle Scholar
  140. 140.
    A. Koga, K. Okunishi, N. Kawakami: Phys. Rev. B 62, 5558 (2000)ADSCrossRefGoogle Scholar
  141. 141.
    J. Schulenburg, J. Richter: Phys. Rev. B 66, 134419 (2002)ADSCrossRefGoogle Scholar
  142. 142.
    C. Gros, W. Wenzel, J. Richter: Europhys. Lett. 32, 747 (1995)ADSCrossRefGoogle Scholar
  143. 143.
    P. Tomczak, J. Richter: J. Phys. A: Math. Gen. 34, L461 (2001)ADSCrossRefGoogle Scholar
  144. 144.
    J. Villain, R. Bidaux, J.P. Carton, R. Conte: J. Phys. 41, 1263 (1980)MathSciNetCrossRefGoogle Scholar
  145. 145.
    E.F. Shender: Zh. Eksp. Teor. Fiz. 83, 326 (1982) (Sov. Phys. JETP 56, 178 (1982))Google Scholar
  146. 146.
    A. Honecker: The magnetization process of antiferromagnetic quantum spin systems and macroscopic quantum effects. habilitation thesis (2003) [http://www.tu-bs.de/~honecker/papers/habil.ps.gz]Google Scholar
  147. 147.
    M. Oshikawa, M. Yamanaka, I. Affleck: Phys. Rev. Lett. 78, 1984 (1997)ADSCrossRefGoogle Scholar
  148. 148.
    A. Honecker, J. Schulenburg, J. Richter: cond-mat/0309425. 2003. to appear in J. Phys. Condens. MatterGoogle Scholar
  149. 149.
    Yu.E. Lozovik, O.I. Notych: Solid State Communications 85, 873 (1993)ADSCrossRefGoogle Scholar
  150. 150.
    M.S. Yang, K.-H. Mütter: Z. Phys. B 104, 117 (1997)ADSCrossRefGoogle Scholar
  151. 151.
    M.E. Zhitomirsky, T. Nikuni: Phys. Rev. B 57, 5013 (1998)ADSCrossRefGoogle Scholar
  152. 152.
    F. Alet, S. Wessel, M. Troyer: cond-mat/0308495. 2003Google Scholar
  153. 153.
    ALPS homepage: http://alps. comp-phys.org/Google Scholar
  154. 154.
    A.W. Sandvik: Phys. Rev. B 59, R14157 (1999)ADSCrossRefGoogle Scholar
  155. 155.
    H. Nishimori, S. Miyashita: J. Phys. Soc. Jpn. 55, 4448 (1986)ADSCrossRefGoogle Scholar
  156. 156.
    A.V. Chubukov, D.I. Golosov: J. Phys.: Condens. Matter 3, 69 (1991)ADSGoogle Scholar
  157. 157.
    K. Hida: J. Phys. Soc. Jpn. 70, 3673 (2001)ADSCrossRefGoogle Scholar
  158. 158.
    J. Schulenburg, A. Honecker, J. Schnack, J. Richter, H.-J. Schmidt: Phys. Rev. Lett. 88, 167207 (2002)ADSCrossRefGoogle Scholar
  159. 159.
    D.C. Cabra, M.D. Grynberg, P.C.W. Holdsworth, P. Pujol: Phys. Rev. B 65, 094418 (2002)ADSCrossRefGoogle Scholar
  160. 160.
    M.E. Zhitomirsky: Phys. Rev. Lett. 88, 057204 (2002)ADSCrossRefGoogle Scholar
  161. 161.
    E.F. Shender, P.C.W. Holdsworth: Order by disorder and topology in frustrated magnetic systems In: Fluctuations and Order ed by M. Millonas (Springer-Verlag, New York 1996) pp 259–279CrossRefGoogle Scholar
  162. 162.
    D.C. Cabra, M.D. Grynberg, P.C.W. Holdsworth, A. Honecker, P. Pujol. J. Richter. J. Schulenburg, in preparation (2004)Google Scholar
  163. 163.
    R. Moessner, S.L. Sondhi: Phys. Rev. B 63, 224401 (2001)ADSCrossRefGoogle Scholar
  164. 164.
    R. Moessner, S.L. Sondhi, P. Chandra: Phys. Rev. B 64, 144416 (2001)ADSCrossRefGoogle Scholar
  165. 165.
    J. Richter, J. Schulenburg, A. Honecker, J. Schnack, H.-J. Schmidt: cond-mat/0309455. 2003, to appear in J. Phys.: Condens. MatterGoogle Scholar
  166. 166.
    J. Schnack, H.-J. Schmidt, J. Richter, J. Schulenburg: Eur. Phys. J. B 24, 475 (2001)ADSCrossRefGoogle Scholar
  167. 167.
    H.-J. Schmidt: J. Phys. A: Math. Gen. 35, 6545 (2002)ADSCrossRefGoogle Scholar
  168. 168.
    M. Oshikawa: Phys. Rev. Lett. 84, 1535 (2000)ADSCrossRefGoogle Scholar
  169. 169.
    J. Richter, O. Derzhko, J. Schulenburg: cond-mat/0312216, 2003Google Scholar
  170. 170.
    T. Momoi, K. Totsuka: Phys. Rev. B 62, 15067 (2000)ADSCrossRefGoogle Scholar
  171. 171.
    S. Gluzman: Phys. Rev. B 50, 6264 (1994)ADSCrossRefGoogle Scholar
  172. 172.
    A. Honecker: Can. J. Phys. 79, 1557 (2001)ADSCrossRefGoogle Scholar
  173. 173.
    G. Jackeli, M.E. Zhitomirsky: cond-mat/0312076, 2003Google Scholar
  174. 174.
    K. Onizuka, H. Kageyama, Y. Narumi, K. Kindo, Y. Ueda, T. Goto: J. Phys. Soc. Jpn. 69, 1016 (2000)ADSCrossRefGoogle Scholar
  175. 175.
    K. Kodama, M. Takigawa, M. Horvatić, C. Berthier, H. Kageyama, Y. Ueda, S. Miyahara, F. Becca, F. Mila: Science 298, 395 (2002)ADSCrossRefGoogle Scholar
  176. 176.
    G.A. Jorge, R. Stern, M. Jaime, N. Harrison, J. Bonča. S. El Shawish, C.D. Batista, H. Dabkowska, B.D. Gaulin: cond-mat/0309534. 2003Google Scholar
  177. 177.
    S. Miyahara, K. Ueda: Phys. Rev. B 61, 3417 (2000)ADSCrossRefGoogle Scholar
  178. 178.
    Y. Fukumoto, A. Oguchi: J. Phys. Soc. Jpn. 69, 1286 (2000)ADSCrossRefGoogle Scholar
  179. 179.
    Y. Fukumoto: J. Phys. Soc. Jpn. 70, 1397 (2001)ADSCrossRefGoogle Scholar
  180. 180.
    C. Knetter, A. Bühler, E. Müller-Hartmann, G.S. Uhrig: Phys. Rev. Lett. 85. 3958 (2000)ADSCrossRefGoogle Scholar
  181. 181.
    H. Kageyama, M. Nishi, N. Aso, K. Onizuka, T. Yosihama, K. Nukui, K. Kodama, K. Kakurai, Y. Ueda: Phys. Rev. Lett. 84, 5876 (2000)ADSCrossRefGoogle Scholar
  182. 182.
    C. Knetter, G.S. Uhrig: Phys. Rev. Lett. 92, 027204 (2004)ADSCrossRefGoogle Scholar
  183. 183.
    S. Miyahara, F. Becca, F. Mila: Phys. Rev. B 68, 024401 (2003)ADSCrossRefGoogle Scholar
  184. 184.
    M.E. Zhitomirsky, A. Honecker, O.A. Petrenko: Phys. Rev. Lett. 85, 3269 (2000)ADSCrossRefGoogle Scholar
  185. 185.
    A. Honecker, O.A. Petrenko, M.E. Zhitomirsky: Physica B 312–313, 609 (2002)CrossRefGoogle Scholar
  186. 186.
    A. Fledderjohann, K.-H. Mütter: Eur. Phys. J. B 24, 211 (2001)ADSCrossRefGoogle Scholar
  187. 187.
    M.-C. Chang, M.-F. Yang: Phys. Rev. B 66, 184416 (2002)ADSCrossRefGoogle Scholar
  188. 188.
    S.E. Palmer, J.T. Chalker: Phys. Rev. B 64, 094412 (2001)ADSCrossRefGoogle Scholar
  189. 189.
    G. Misguich, B. Bernu, C. Lhuillier, C. Waldtmann: Phys. Rev. Lett. 81, 1098 (1998)ADSCrossRefGoogle Scholar
  190. 190.
    T. Momoi, H. Sakamoto, K. Kubo: Phys. Rev. B 59, 9491 (1999)ADSCrossRefGoogle Scholar
  191. 191.
    K. Kubo, T. Momoi: Z. Phys. B 103, 485 (1997)ADSCrossRefGoogle Scholar
  192. 192.
    V.N. Popov: Theor. Math. Phys. 11, 565 (1972)CrossRefGoogle Scholar
  193. 193.
    S. Gluzman: Z. Phys. B 90, 313 (1993)ADSCrossRefGoogle Scholar
  194. 194.
    S. Sachdev, T. Senthil, R. Shankar: Phys. Rev. B 50, 258 (1994)ADSCrossRefGoogle Scholar

Copyright information

© Springer-Verlag 2004

Authors and Affiliations

  • Johannes Richter
    • 1
  • Jörg Schulenburg
    • 2
  • Andreas Honecker
    • 3
  1. 1.Institut für Theoretische PhysikOtto-von-Guericke-Universität MagdeburgMagdeburgGermany
  2. 2.UniversitätsrechenzentrumOtto-von-Guericke-Universität MagdeburgMagdeburgGermany
  3. 3.Institut für Theoretische PhysikTU BraunschweigBraunschweigGermany

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