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

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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.

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Authors and Affiliations

  1. C. N. Yang Institute for Theoretical Physics, State University of New York at Stony Brook, Stony Brook, New York, 11794-3840

    B.-Q. Jin & V. E. Korepin

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  1. B.-Q. Jin
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  2. V. E. Korepin
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Jin, BQ., Korepin, V.E. Quantum Spin Chain, Toeplitz Determinants and the Fisher—Hartwig Conjecture. Journal of Statistical Physics 116, 79–95 (2004). https://doi.org/10.1023/B:JOSS.0000037230.37166.42

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  • DOI: https://doi.org/10.1023/B:JOSS.0000037230.37166.42

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