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We consider a chaotic many-body system (i.e., one that satisfies the eigenstate thermalization hypothesis) that is split into two subsystems, with an interaction along their mutual boundary, and study the entanglement properties of an energy eigenstate with nonzero energy density.
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L. Amico, R. Fazio, A. Osterloh, and V. Vedral, Entanglement in many-body systems, Reviews of Modern Physics 80
2008
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J. M. Deutsch, Thermodynamic entropy of a many-body energy eigenstate, New Journal of Physics 12
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2010
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2012
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2017
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2018
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2018
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2018
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T. C. Lu and T. Grover, Renyi entropy of chaotic eigenstates, Physical Review E 99
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2013
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2015
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Note that the eigenstate expectation value ⟨ E | h x h y | E ⟩ \langle E|h_{x}h_{y}|E\rangle must in general differ from the thermal expectation value ⟨ h x h y ⟩ \langle h_{x}h_{y}\rangle by O ( 1 / V ) O(1/V) , even when | x − y | ≫ ξ |x-y|\gg\xi ; this is needed to recover ⟨ E | ( H − E ) 2 | E ⟩ = 0 \langle E|(H-E)^{2}|E\rangle=0 . However, this difference only contributes an O ( A / V ) O(A/V) correction to Eq. ( 37
Cited in the paper.
More precisely, the third and higher cumulants of H 12 / Δ H_{12}/\Delta in the state | E ⟩ |E\rangle are suppressed relative to the variance, ⟨ E | ( H 12 / Δ ) 2 | E ⟩ ≡ 1 \langle E|(H_{12}/\Delta)^{2}|E\rangle\equiv 1 , by powers of 1 / A 1/\sqrt{A}
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2019
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