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.
Highlights
Entanglement entropy (EE) provides important information of a given state, in particular, correlations in a ground state between two spatially separated regions and has been widely discussed in quantum information, condensed matter physics and, even in quantum gravity, cosmology, and high energy physics [1,2,3,4,5,6,7,8,9,10,11,12]
We consider EE of a half space in an interacting scalar field theory. It is formulated as ZM gauge theory on Feynman diagrams: ZM fluxes are assigned on plaquettes and summed to obtain EE
The practical computation of EE in field theories is not an easy task and much of the works have focused on Gaussian states [13,14,15,16,17,18,19], low-energy sectors of conformal field theories (CFTs) [5,20,21,22] or holographic CFTs [6,7,23]
Summary
Entanglement entropy (EE) provides important information of a given state, in particular, correlations in a ground state between two spatially separated regions and has been widely discussed in quantum information, condensed matter physics and, even in quantum gravity, cosmology, and high energy physics [1,2,3,4,5,6,7,8,9,10,11,12]. Our goal in this paper is to provide a field theoretic, systematic way to explore EE in a massive interacting theory, which is neither free nor conformally invariant and the existence of its holographic dual is not assumed. There are additional UV divergences in interacting field theories, which should be dealt with the usual flat space renormalization. We consider a scalar field theory with φ4 interactions in a simple geometrical setup, a half space being traced over. It is formulated as a ZM gauge theory on Feynman diagrams: We perturbatively evaluate EE in the two-particle irreducible (2PI) formalism and obtain a generalized 1-loop type expression of EE in terms of renormalized propagators. The EE can be rewritten in terms of the free energy Fn ≡ − log Zn ≡ − log TrAρnA as SA 1⁄4 ∂Fn=∂njn→1 − F1
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