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)


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


Correlation Length Loop Algorithm Monte Carlo Step Exact Diagonalization Spin Configuration 
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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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