# 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) 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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