Entanglement Entropy in the O(N) Model

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Entanglement Entropy in the O(N) Model

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Title: Entanglement Entropy in the O(N) Model
Author: Metlitski, Max; Fuertes, Carlos; Sachdev, Subir

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Citation: Metlitski, Max, Carlos A. Fuertes, and Subir Sachdev. 2009. Entanglement Entropy in the O(N) model. Physical Review B 80(11): 115122.
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Abstract: It is generally believed that in spatial dimension \(d\) > 1 the leading contribution to the entanglement entropy \(S = - tr\rho_A log \rho_A\) scales as the area of the boundary of subsystem \(A\). The coefficient of this "area law" is non-universal. However, in the neighbourhood of a quantum critical point \(S\) is believed to possess subleading universal corrections. In the present work, we study the entanglement entropy in the quantum \(O(N)\) model in 1 < \(d\) < 3. We use an expansion in \(\epsilon = 3-d\) to evaluate i) the universal geometric correction to \(S\) for an infinite cylinder divided along a circular boundary; ii) the universal correction to \(S\) due to a finite correlation length. Both corrections are different at the Wilson-Fisher and Gaussian fixed points, and the \(\epsilon \to 0\) limit of the Wilson-Fisher fixed point is distinct from the Gaussian fixed point. In addition, we compute the correlation length correction to the Renyi entropy \(S_n = 1/1-n log tr {\rho_A}^n\) in \(\epsilon\) and large-\(N\) expansions. For \(N \to \infty\), this correction generally scales as \(N^2\) rather than the naively expected \(N\). Moreover, the Renyi entropy has a phase transition as a function of \(n\) for \(d\) close to 3.
Published Version: doi:10.1103/PhysRevB.80.115122
Other Sources: http://arxiv.org/abs/0904.4477v1
Terms of Use: This article is made available under the terms and conditions applicable to Open Access Policy Articles, as set forth at http://nrs.harvard.edu/urn-3:HUL.InstRepos:dash.current.terms-of-use#OAP
Citable link to this page: http://nrs.harvard.edu/urn-3:HUL.InstRepos:7617043
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