Probing trihedral corner entanglement for Dirac fermions

TL;DR

This paper explores the universal aspects of entanglement entropy in a 3D Dirac fermion system, revealing how trihedral corners contribute a universal logarithmic term linked to critical theory parameters.

Contribution

It provides the first numerical evidence that trihedral corner contributions to entanglement entropy are universal and related to the underlying critical theory and geometry.

Findings

Corner contributions grow logarithmically with subsystem size.

Universal coefficients are determined by critical theory functions.

Corner contributions may help determine universal central charges.

Abstract

We investigate the universal information contained in the Renyi entanglement entropies for a free massless Dirac fermion in three spatial dimensions. Using numerical calculations on the lattice, we examine the case where the entangling boundary contains trihedral corners. The entropy contribution arising from these corners grows logarithmically in the entangled subsystem's size with a universal coefficient. Our numerical results provide evidence that this logarithmic coefficient has a simple structure determined by two universal functions characterizing the underlying critical theory and the geometry of the corner. This form is similar to that of the analogous coefficient appearing for smooth entangling surfaces. Furthermore, our results support the idea that one of the geometric factors in the corner coefficient is topological in nature and related to the Euler characteristic of the boundary, in direct analogy to the case of the smooth surface. We discuss implications, including the possibility that one can use trihedral corner contributions to the Renyi entropy to determine both of the universal central charges of the underlying critical theory.