Journal of Statistical Physics

, Volume 116, Issue 1–4, pp 79–95

Quantum Spin Chain, Toeplitz Determinants and the Fisher—Hartwig Conjecture

  • B.-Q. Jin
  • V. E. Korepin


We consider the one-dimensional quantum spin chain, which is called the XX model (XX0 model or isotropic XY model) in a transverse magnetic field. We are mainly interested in the entropy of a block of Lneighboring spins at zero temperature and of an infinite system. We represent the entropy in terms of a Toeplitz determinant and calculate the asymptotic analytically. We derive the first two terms of the asymptotic decomposition. Interestingly, these two terms of decomposition clearly show a length scale related to the field h.

quantum spin chain XX0 model entropy Toeplitz determinant quantum entanglement 


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Copyright information

© Plenum Publishing Corporation 2004

Authors and Affiliations

  • B.-Q. Jin
    • 1
  • V. E. Korepin
    • 1
  1. 1.C. N. Yang Institute for Theoretical PhysicsState University of New York at Stony BrookStony Brook

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