Smooth Perturbations to Rényi Entropy

Abstract

A method is presented for computing the Rényi 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 Rényi entropy are analytically computable for all Rényi parameter $\hat{I}\pm$ in odd dimensions and for integer $\hat{I}\pm$ in even dimensions. I apply this procedure to compute coefficients for the large distant expansion for the Rényi mutual information of distant balls and the low temperature expansion for the entropy of a thermal field.

Main: 16 pages, 1 figure; Appendix: 20 pages, 3 figures