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