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This is an extended version of the previous paper arXiv:2103.05303 to studyentanglement entropy (EE) of a half space in interacting field theories. In theprevious paper, we have proposed a novel method to calculate EE based on thenotion of $\mathbb{Z}_M$ gauge theory on Feynman diagrams, and shown that EEconsists of two particular contributions, one from a renormalized two-pointcorrelation function in the two-particle irreducible (2PI) formalism andanother from interaction vertices. In this paper, we further investigate themin more general field theories and show that the non-Gaussian contributionsfrom vertices can be interpreted as renormalized correlation functions ofcomposite operators.

Non-Gaussianity of Entanglement Entropy and Correlations of Composite Operators