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 λare 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=-lnρwith reduced density matrix ρwhich corresponds to a semi-infinite part of the model in the ground state. It is shown that in the vicinity of a critical point λ_c=1, the entanglement entropy fluctuation ΔS (square root of dispersion) diverges as \Delts S\sim[ln(1/|1-λ|)]^{1/2}. Taking into account the known behavior of the entanglement entropy S, this leads to that the value of relative entanglement fluctuation δS=(ΔS)/S vanishes at the critical point, i.e. in fact a state with nonfluctuating entanglement is realized.

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