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Entanglement entropy fluctuations in quantum Ising chains

  • Atoms, Molecules, Optics
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Abstract

The behavior of Ising chains with the spin-spin interaction value λ in a transverse magnetic field of constant intensity (h = 1) is considered. For a chain of infinite length, exact analytical formulas are obtained for the second central moment (dispersion) of the entropy operator Ŝ = -lnρ with reduced density matrix ρ, which corresponds to a semi-infinite part of the model chain occurring in the ground state. In the vicinity of a critical point λc = 1, the entanglement entropy fluctuation ΔS (defined as the square root of dispersion) diverges as ΔS ∼ [ln(1/|1 − λ|)]1/2. For the known behavior of the entanglement entropy S, this divergence results in that the relative fluctuation δS = ΔS/S vanishes at the critical point, that is, a state with almost nonfluctuating entanglement is attained.

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Authors and Affiliations

  1. Institute of Problems of Chemical Physics, Russian Academy of Sciences, Chernogolovka, Moscow oblast, 142432, Russia

    M. A. Yurishchev

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Correspondence to M. A. Yurishchev.

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Original Russian Text © M.A. Yurishchev, 2010, published in Zhurnal Éksperimental’noĭ i Teoreticheskoĭ Fiziki, 2010, Vol. 138, No. 4, pp. 595–604.

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Yurishchev, M.A. Entanglement entropy fluctuations in quantum Ising chains. J. Exp. Theor. Phys. 111, 525–533 (2010). https://doi.org/10.1134/S1063776110100018

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