Entanglement, Toeplitz Determinants and Fisher-Hartwig Conjecture

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Abstract
We consider the one-dimensional quantum spin chain. It is called the XX model in a transverse magnetic field. We are interested in the case of zero temperature and infinite volume. We study entanglement of a block of L neighboring spins with the rest of the system. We represent the entanglement in terms of a Toeplitz determinant and study the entanglement of large blocks asymptotically. We derive the first two terms of the asymptotic decomposition analytically.

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