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Parallel Quantum Monte Carlo Simulation of S = 3 Antiferromagnetic Heisenberg Chain

Conference paper
Part of the Springer Proceedings in Physics book series (SPPHY, volume 90)

Abstract

Since Haidane made a striking conjecture that the integer-spin (S = 1, 2, 3, …) antiferromagnetic Heisenberg chain has a finite excitation gap above its unique ground state [1], estimation of its precise value has been one of the most challenging problems in the computational condensed-matter physics. For the spin-1 system the finiteness of the first excitation gap as well as the correlation length has been established numerically until early 90s [2]. Simulations of higher-spin systems, however, are much harder since the magnitudes of the inversed gap and the correlation length would increase exponentially as S increases. Indeed the asymptotic forms for the large-S limit [1] suggests that in the spin-3 case they are of order 102 and 103, respectively

Keywords

Correlation Length Loop Algorithm Monte Carlo Step Exact Diagonalization Spin Configuration 
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.
    F.D.M. Haidane: Phys. Lett. 93A, 464 (1983); Phys. Rev. Lett. 50, 1153 (1983)ADSGoogle Scholar
  2. 2.
    See, e.g. S.R. White and D.A. Huse: Phys. Rev. B 48, 3844 (1993); O. Golinelli, Th. Jolicceur, and R. Lacaze: Phys. Rev. B 50, 3037 (1994)ADSCrossRefGoogle Scholar
  3. 3.
    See, e.g. S. Todo, M. Matsumoto, C. Yasuda, and H. Takayama: Phys. Rev. B 64, 224412 (2002)ADSCrossRefGoogle Scholar
  4. 4.
    S. Todo and K. Kato: Phys. Rev. Lett. 87, 047203 (2001)ADSCrossRefGoogle Scholar
  5. 5.
    H.G. Evertz, G. Lana, and M. Marcu: Phys. Rev. Lett. 70, 875 (1993); U.-J. Wiese and H.-P. Ying: Z. Phys. B 93, 147 (1994)ADSCrossRefGoogle Scholar
  6. 6.
    B.B. Beard and U.-J. Wiese: Phys. Rev. Lett. 77, 5130 (1996)ADSCrossRefGoogle Scholar
  7. 7.
    N. Kawashima and J.E. Gubernatis: Phys. Rev. Lett. 73, 1295 (1994); J. Stat. Phys. 80, 169 (1995); K. Harada, M. Troyer, and N. Kawashima: J. Phys. Soc. Jpn. 67, 1130 (1998)ADSCrossRefGoogle Scholar
  8. 8.
    F. Cooper, B. Freedman, and D. Preston: Nucl. Phys. B 210[FS6], 210 (1982)ADSCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  • S. Todo
    • 1
    • 2
  1. 1.Theoretische PhysikEidgenössische Technische HochschuleZürichSwitzerland
  2. 2.Institute for Solid State PhysicsUniversity of TokyoKashiwaJapan

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