The Fisher-Hartwig Formula and Generalized Entropies in XY Spin Chain
A. R. Its, V. E. Korepin
TL;DR
This paper applies the Fisher-Hartwig formula to compute entanglement and Renyi entropies in the XY spin chain, revealing the spectrum's geometric nature and degeneracy patterns of the density matrix.
Contribution
It introduces a novel application of the Fisher-Hartwig formula to analyze entanglement in the XY spin chain, providing exact spectral results.
Findings
Entanglement entropy computed using Fisher-Hartwig formula
Renyi entropy calculated for large spin blocks
Density matrix spectrum shown to be an exact geometric sequence
Abstract
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].
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Taxonomy
TopicsQuantum many-body systems · Quantum Information and Cryptography · Neural Networks and Reservoir Computing