Euclidean Time Approach to Entanglement Entropy on Lattices and Fuzzy Spaces

TL;DR

This paper introduces a Euclidean time method for calculating entanglement entropy on lattices and fuzzy spaces, providing proofs and applications for scalar theories, including interacting models, and extending to fuzzy geometries.

Contribution

It presents a new Euclidean time approach for entanglement entropy computation, including proof of Green's function formula and applications to interacting scalar theories on lattices and fuzzy spaces.

Findings

Validated the Green's matrix function formula.

Confirmed first-order corrections to entanglement entropy in interacting models.

Outlined methods for entanglement entropy calculation on fuzzy spaces.

Abstract

In a recent letter, we developed a novel Euclidean time approach to compute R\'{e}nyi entanglement entropy on lattices and fuzzy spaces based on Green's function. The present work is devoted in part to the explicit proof of the Green's matrix function formula which was quoted and used in the previous letter, and on the other part to some applications of this formalism. We focus on scalar theory on 1+1 lattice. We also use the developed approach to go systematically beyond the Gaussian case by considering interacting models, in particular our results confirm earlier expectations concerning the correction to the entanglement at first order. We finally outline how this approach can be used to compute the entanglement entropy on fuzzy spaces for free and interacting scalar theories.