Quantum Spin Chain, Toeplitz Determinants and the Fisher—Hartwig Conjecture
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- Jin, B. & Korepin, V.E. Journal of Statistical Physics (2004) 116: 79. doi:10.1023/B:JOSS.0000037230.37166.42
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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.