Green’s Function Approach to Entanglement Entropy on Lattices

Abstract

We develop a Green’s function approach to compute Rényi entanglement entropy on lattices. The Rényi entropy resulting from tracing out an arbitrary collection of subsets of coupled harmonic oscillators is written as zero temperature partition function generated by an Euclidean action with n-fold step potential. The associated Green’s function is explicitly constructed and an alternative new formula for the Rényi entropy is obtained. To show the applicability of the method we take the example of 2-coupled harmonic oscillator as an application.