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arXiv · 1509.05685

Entanglement Entropy and Variational Methods: Interacting Scalar Fields

Jordan Cotler·Mark T. Mueller
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Abstract

We develop a variational approximation to the entanglement entropy for scalar $\phi^4$ theory in 1+1, 2+1, and 3+1 dimensions, and then examine the entanglement entropy as a function of the coupling. We find that in 1+1 and 2+1 dimensions, the entanglement entropy of $\phi^4$ theory as a function of coupling is monotonically decreasing and convex. While $\phi^4$ theory with positive bare coupling in 3+1 dimensions is thought to lead to a trivial free theory, we analyze a version of $\phi^4$ with infinitesimal negative bare coupling, an asymptotically free theory known as precarious $\phi^4$ theory, and explore the monotonicity and convexity of its entanglement entropy as a function of coupling. Within the variational approximation, the stability of precarious $\phi^4$ theory is related to the sign of the first and second derivatives of the entanglement entropy with respect to the coupling.

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Jordan Cotler, Mark T. Mueller. 2015-09-18. Entanglement Entropy and Variational Methods: Interacting Scalar Fields. https://doi.org/10.1016/j.aop.2015.12.005

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