Numerical determination of the entanglement entropy for free fields in the cylinder

TL;DR

This paper numerically computes the universal logarithmic term of entanglement entropy for free scalar and Dirac fields in a cylindrical region, confirming analytical predictions and exploring mass corrections via dimensional reduction.

Contribution

It provides the first numerical verification of the universal entanglement entropy coefficient for free fields in a cylinder and links it to mass corrections through dimensional reduction.

Findings

Confirmed the universal coefficient matches conformal anomaly predictions.

Validated the dimensional reduction approach for entanglement entropy.

Cross-checked results for scalar and Dirac fields independently.

Abstract

We calculate numerically the logarithmic contribution to the entanglement entropy of a cylindrical region in three spatial dimensions for both, free scalar and Dirac fields. The coefficient is universal and proportional to the type $c$ conformal anomaly in agreement with recent analytical predictions. We also calculate the mass corrections to the entanglement entropy for scalar and Dirac fields in a disk. These apparently unrelated problems make contact through the dimensional reduction procedure valid for free fields whereby the entanglement entropy for the cylinder can be calculated as an integral over masses of the disk entanglement entropies. Coming from the same numerical evaluation in the lattice, each coefficient is cross checked by the other, testing in this way the two results simultaneously.