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Entanglement Entropy and Variational Methods: Interacting Scalar Fields | Jordan Cotler
; Mark T. Mueller
; | Date: |
18 Sep 2015 | 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. | Source: | arXiv, 1509.5685 | Services: | Forum | Review | PDF | Favorites |
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