Smooth Perturbations to R\'enyi Entropy

TL;DR

This paper introduces an analytical method to compute Re9nyi entropy for perturbed vacuum states in quantum field theory, enabling calculations for various dimensions and parameters, with applications to mutual information and thermal entropy.

Contribution

It provides a novel analytical approach to calculate Re9nyi entropy coefficients for Gaussian states with smooth perturbations across different dimensions and parameters.

Findings

Coefficients are analytically computable for all e9nyi b5 in odd dimensions.

Coefficients are computable for integer e9nyi b5 in even dimensions.

Applications include large-distance mutual information and low-temperature thermal entropy expansions.

Abstract

A method is presented for computing the R\'enyi entropy of a perturbed massless vacuum on the ball via a comparison with lattice field theory. If the perturbed state is Gaussian with smoothly varying correlation functions and the perturbation parameter has units of energy, I show the coefficients for R\'enyi entropy are analytically computable for all R\'enyi parameter $\alpha$ in odd dimensions and for integer $\alpha$ in even dimensions. I apply this procedure to compute coefficients for the large distant expansion for the R\'enyi mutual information of distant balls and the low temperature expansion for the entropy of a thermal field.