Article

Journal of Statistical Physics

, Volume 116, Issue 1, pp 79-95

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

  • B.-Q. JinAffiliated withC. N. Yang Institute for Theoretical Physics, State University of New York at Stony Brook
  • , V. E. KorepinAffiliated withC. N. Yang Institute for Theoretical Physics, State University of New York at Stony Brook

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Abstract

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