Euclidean time approach to entanglement entropy on lattices and fuzzy spaces

Abstract

Abstract In a recent letter, Phys. Lett. B792 (2019) 60, we developed a novel Euclidean time approach to compute Rényi 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 systematically go 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.