Geodesic
Generalized entropy of the Heisenberg spin chain
Teoretičeskaâ i matematičeskaâ fizika, Tome 164 (2010) no. 3, pp. 363-367 Cet article a éte moissonné depuis la source Math-Net.Ru

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We consider the XY quantum spin chain in a transverse magnetic field. We consider the Rényi entropy of a block of neighboring spins at zero temperature on an infinite lattice. the Rényi entropy is essentially the trace of some power $\alpha$ of the density matrix of the block. We calculate the entropy of the large block in terms of Klein's elliptic $\lambda$-function. We study the limit entropy as a function of its parameter $\alpha$. We show that the Rényi entropy is essentially an automorphic function with respect to a certain subgroup of the modular group. Using this, we derive the transformation properties of the Rényi entropy under the map $\alpha\to\alpha^{-1}$.
Mots-clés : quantum entanglement, spin chain
Keywords: Bethe ansatz. 
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A. R. Its; V. E. Korepin. Generalized entropy of the Heisenberg spin chain. Teoretičeskaâ i matematičeskaâ fizika, Tome 164 (2010) no. 3, pp. 363-367. http://geodesic.mathdoc.fr/item/TMF_2010_164_3_a3/

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