Entanglement entropy in interacting field theories

Entanglement entropy (EE) in interacting field theories has two important issues: renormalization of UV divergences and non-Gaussianity of the vacuum. In this paper, 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.Entanglement entropy (EE) in interacting field theories has two important issues: renormalization of UV divergences and non-Gaussianity of the vacuum. In this paper, 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.

arXiv:2103.05303Physical review. D/Physical review. D.May 17, 202110 citations

Entanglement Entropy in Lattice Theories

Mihael Hategan

Jan 1, 20190 citations

Non-Gaussianity of entanglement entropy and correlations of composite operators

Satoshi Iso, Takato Mori, K. Sakai

This is an extended version of the previous paper [S. Iso et al., Phys. Rev. D 103, 105010 (2021)] 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.This is an extended version of the previous paper [S. Iso et al., Phys. Rev. D 103, 105010 (2021)] 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.

arXiv:2105.02598Physical review. D/Physical review. D.Jun 22, 202110 citations

Observations on entanglement entropy in massive QFT’s

Aitor Lewkowycz, Robert Cobb Myers, Michael Smolkin

arXiv:1210.6858Journal of High Energy PhysicsApr 1, 201364 citations

Theory of Entanglement Entropy

Durrani, Ijaz

Jan 1, 20250 citations

Wilsonian Effective Action and Entanglement Entropy

Satoshi Iso, Takato Mori, K. Sakai

This is a continuation of our previous works on entanglement entropy (EE) in interacting field theories. In previous papers, we have proposed the notion of ZM gauge theory on Feynman diagrams to calculate EE in quantum field theories and shown that EE consists of two particular contributions from propagators and vertices. We have also shown that the purely non-Gaussian contributions from interaction vertices can be interpreted as renormalized correlation functions of composite operators. In this paper, we will first provide a unified matrix form of EE containing both contributions from propagators and (classical) vertices, and then extract further non-Gaussian contributions based on the framework of the Wilsonian renormalization group. It is conjectured that the EE in the infrared is given by a sum of all the vertex contributions in the Wilsonian effective action.This is a continuation of our previous works on entanglement entropy (EE) in interacting field theories. In previous papers, we have proposed the notion of ZM gauge theory on Feynman diagrams to calculate EE in quantum field theories and shown that EE consists of two particular contributions from propagators and vertices. We have also shown that the purely non-Gaussian contributions from interaction vertices can be interpreted as renormalized correlation functions of composite operators. In this paper, we will first provide a unified matrix form of EE containing both contributions from propagators and (classical) vertices, and then extract further non-Gaussian contributions based on the framework of the Wilsonian renormalization group. It is conjectured that the EE in the infrared is given by a sum of all the vertex contributions in the Wilsonian effective action.

arXiv:2105.14834SymmetryJul 7, 202110 citations

{\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.

{\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.