Entanglement entropy in scalar field theory and ${\mathbb{Z}}_M$ gauge theory on Feynman diagrams

Abstract

Entanglement entropy (EE) in interacting field theories has two important issues: renormalization of UV divergences and non-Gaussianity of the vacuum. In this letter, we investigate them in the framework of the two-particle irreducible formalism. In particular, we consider EE of a half space in an interacting scalar field theory. It is formulated as ${\mathbb{Z}}_M$ gauge theory on Feynman diagrams: ${\mathbb{Z}}_M$ fluxes are assigned on plaquettes and summed to obtain EE. Some configurations of fluxes are interpreted as twists of propagators and vertices. The former gives a Gaussian part of EE written in terms of a renormalized 2-point function while the latter reflects non-Gaussianity of the vacuum.

7 pages, 8 figures; detailed derivations of equations and 4 figures added (v2); minor corrections, published version in PRD (v3)

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• Wilsonian Effective Action and Entanglement Entropy
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• Wilsonian Renormalization as a Quantum Channel and the Separability of Fixed Points
• Non-Conformal Behavior of Holographic Entanglement Measures
• The Large $N$ Limit of icMERA and Holography
• Entanglement Entropy of $(2+1)$D Quantum Critical Points with Quenched Disorder: Dimensional Reduction Approach
• Towards Entanglement Entropy of Random Large-N Theories