Entanglement Entropy Fluctuations in Quantum Ising Chains

The Ising chains in a transverse magnetic field of constant strength (h=1) and with the spin interaction value \lambda are considered. In the case of infinitely long chain, exact analytical expressions are found for the second central moment (dispersion) of the entropy operator S^\hat=-ln\rho with r...

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Bibliographic Details
Published in:arXiv.org 2010-11
Main Author: Yurishchev, M A
Format: Article
Language:English
Subjects:
Chain entanglement
Chains
Critical point
Dispersion
Entanglement
Entropy
Ising model
Mathematical analysis
Variation
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Summary:The Ising chains in a transverse magnetic field of constant strength (h=1) and with the spin interaction value \lambda are considered. In the case of infinitely long chain, exact analytical expressions are found for the second central moment (dispersion) of the entropy operator S^\hat=-ln\rho with reduced density matrix \rho which corresponds to a semi-infinite part of the model in the ground state. It is shown that in the vicinity of a critical point \lambda_c=1, the entanglement entropy fluctuation \Delta S (square root of dispersion) diverges as \Delts S\sim[ln(1/|1-\lambda|)]^{1/2}. Taking into account the known behavior of the entanglement entropy S, this leads to that the value of relative entanglement fluctuation \delta S=(\Delta S)/S vanishes at the critical point, i.e. in fact a state with nonfluctuating entanglement is realized.
ISSN:2331-8422
DOI:10.48550/arxiv.1011.4165