Time evolution of entanglement entropy of moving mirrors influenced by strongly coupled quantum critical fields

Journal of High Energy Physics, Jun 2019

Abstract The evolution of the Von Neumann entanglement entropy of a n-dimensional mirror influenced by the strongly coupled d-dimensional quantum critical fields with a dynamic exponent z is studied by the holographic approach. The dual description is a n+1-dimensional probe brane moving in the d+1-dimensional asymptotic Lifshitz geometry ended at r = rb, which plays a role as the UV energy cutoff. Using the holographic influence functional method, we find that in the linear response region, by introducing a harmonic trap for the mirror, which serves as a IR energy cutoff, the Von Neumann entropy at late times will saturate by a power-law in time for generic values of z and n. The saturated value and the relaxation rate depend on the parameter α ≡ 1+(n+2)/z, which is restricted to 1 < α < 3 but α = 2. We find that the saturated values of the entropy are qualitatively different for the theories with 1 < α < 2 and 2 < α < 3. Additionally, the power law relaxation follows the rate ∝ t−2α−1. This probe brane approach provides an alternative way to study the time evolution of the entanglement entropy in the linear response region that shows the similar power-law relaxation behavior as in the studies of entanglement entropies based on Ryu-Takayanagi conjecture. We also compare our results with quantum Brownian motion in a bath of relativistic free fields.

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Time evolution of entanglement entropy of moving mirrors influenced by strongly coupled quantum critical fields

Journal of High Energy Physics June 2019, 2019:68 | Cite as Time evolution of entanglement entropy of moving mirrors influenced by strongly coupled quantum critical fields AuthorsAuthors and affiliations Da-Shin LeeChen-Pin Yeh Open Access Regular Article - Theoretical Physics First Online: 14 June 2019 19 Downloads Abstract The evolution of the Von Neumann entanglement entropy of a n-dimensional mirror influenced by the strongly coupled d-dimensional quantum critical fields with a dynamic exponent z is studied by the holographic approach. The dual description is a n+1-dimensional probe brane moving in the d+1-dimensional asymptotic Lifshitz geometry ended at r = rb, which plays a role as the UV energy cutoff. Using the holographic influence functional method, we find that in the linear response region, by introducing a harmonic trap for the mirror, which serves as a IR energy cutoff, the Von Neumann entropy at late times will saturate by a power-law in time for generic values of z and n. The saturated value and the relaxation rate depend on the parameter α ≡ 1+(n+2)/z, which is restricted to 1 < α < 3 but α = 2. We find that the saturated values of the entropy are qualitatively different for the theories with 1 < α < 2 and 2 < α < 3. Additionally, the power law relaxation follows the rate ∝ t−2α−1. This probe brane approach provides an alternative way to study the time evolution of the entanglement entropy in the linear response region that shows the similar power-law relaxation behavior as in the studies of entanglement entropies based on Ryu-Takayanagi conjecture. We also compare our results with quantum Brownian motion in a bath of relativistic free fields. 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Da-Shin Lee, Chen-Pin Yeh. Time evolution of entanglement entropy of moving mirrors influenced by strongly coupled quantum critical fields, Journal of High Energy Physics, 2019, 68, DOI: 10.1007/JHEP06(2019)068