Green's Function Approach to Entanglement Entropy on Lattices and Fuzzy Spaces

Abstract

We develop a Green's function approach to compute Rényi entanglement entropy on lattices and fuzzy spaces. 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. Finally it is outlined how this approach can be used to go beyond the gaussian state and include interaction by writing a perturbative expansion for the entanglement entropy .

Comments: Replacement of the earlier version. Eq (23) and Eq (24) fixed