Entanglement entropy and variational methods: Interacting scalar fields |
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Authors: | Jordan S Cotler Mark T Mueller |
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Institution: | 1. Stanford Institute for Theoretical Physics, Department of Physics, Stanford University, United States;2. Center for Theoretical Physics, Department of Physics, Massachusetts Institute of Technology, United States |
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Abstract: | We develop a variational approximation to the entanglement entropy for scalar ?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 ?4 theory as a function of coupling is monotonically decreasing and convex. While ?4 theory with positive bare coupling in 3+1 dimensions is thought to lead to a trivial free theory, we analyze a version of ?4 with infinitesimal negative bare coupling, an asymptotically free theory known as precarious ?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 ?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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Keywords: | Entanglement Entropy Quantum field theory Variational principles |
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