Entanglement Entropy in the O(N) Model
| Title: | Entanglement Entropy in the O(N) Model |
| Author: |
Metlitski, Max; Fuertes, Carlos; Sachdev, Subir
Note: Order does not necessarily reflect citation order of authors. |
| Citation: | Metlitski, Max, Carlos A. Fuertes, and Subir Sachdev. 2009. Entanglement Entropy in the O(N) model. Physical Review B 80(11): 115122. |
| Full Text & Related Files: |
0904.4477v1.pdf (414.5Kb; PDF) 
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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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