Numerical determination of entanglement entropy for a sphere

TL;DR

This paper numerically computes the entanglement entropy's logarithmic coefficient for a scalar field in a sphere, confirming the analytical value with high precision using Srednicki's regularization.

Contribution

It provides a high-accuracy numerical verification of the analytical logarithmic coefficient in entanglement entropy for a scalar field in a spherical region.

Findings

Coefficient of logarithm is approximately -1/90

Numerical results agree with analytical predictions within 0.2%

Validates Srednicki's regularization method for this calculation

Abstract

We apply Srednicki's regularization to extract the logarithmic term in the entanglement entropy produced by tracing out a real, massless, scalar field inside a three dimensional sphere in 3+1 flat spacetime. We find numerically that the coefficient of the logarithm is -1/90 to 0.2 percent accuracy, in agreement with an existing analytical result.