Green's Function Approach to Entanglement Entropy on Lattices and Fuzzy Spaces
Abstract
We develop a Green's function approach to compute R\'enyi entanglement entropy on lattices and fuzzy spaces. The R\'enyi 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 R\'enyi 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 .
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