Spectrum of the density matrix of a large block of spins of the XY model in one dimension
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.