The Fisher-Hartwig Formula and Generalized Entropies in XY Spin Chain
نویسندگان
چکیده
Toeplitz matrices have applications to different problems of statistical mechanics. Recently it was used for calculation of entanglement entropy in exactly solvable models including spin chains. We use Fisher-Hartwig formula to calculate entanglement entropy [as well as Rényi entropy] of large block of spins in the ground state of XY spin chain. In the end of the paper we announce our recent results [with F. Franchini and L. A. Takhtajan] on spectrum of density matrix of the block of spins.
منابع مشابه
Fisher - Hartwig Formula and Entanglement entropy
Toeplitz matrices have applications to different problems of statistical mechanics. Recently it was used for calculation of entanglement entropy in spin chains. In the paper we review these recent developments. We use Fisher-Hartwig formula, as well as the recent results concerning the asymp-totics of the block Toeplitz determinants, to calculate entanglement entropy of large block of spins in ...
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متن کاملar X iv : c on d - m at / 9 90 83 26 v 3 2 N ov 1 99 9 Gaudin Hypothesis for the XY Z Spin Chain
The XY Z spin chain is considered in the framework of the generalized algebraic Bethe ansatz developed by Takhtajan and Faddeev. The sum of norms of the Bethe vectors is computed and expressed in the form of a Jacobian. This result corresponds to the Gaudin hypothesis for the XY Z spin chain.
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