The Fisher-Hartwig Formula and Generalized Entropies in XY Spin Chain

Understand

Toeplitz matrices have applications to different problems of statistical mechanics.

• Recently they were used for calculation of entanglement entropy in spin chains.
• We use the Fisher-Hartwig formula to calculate entanglement entropy of large block of spins in the ground state of XY spin chain.
• We also calculate Renyi entropy and prove that the spectrum of the density matrix of a block of spins is exact geometric sequence [also different eigenvalues are degenerated differently].