Quantum Entanglement on Boundaries

TL;DR

This paper investigates universal boundary effects on quantum entanglement entropy in 3D systems with boundaries, deriving new boundary terms and exploring their dependence on geometry and field types.

Contribution

It derives universal logarithmic boundary terms in entanglement Rényi entropy for various conformal field theories and geometries, expanding understanding of boundary entanglement effects.

Findings

Universal boundary logarithmic terms in entanglement entropy derived.

Dependence of entropy on boundary and entangling surface geometry analyzed.

Relations established between trace anomaly coefficients and boundary entropy terms.

Abstract

Quantum entanglement in 3 spatial dimensions is studied in systems with physical boundaries when an entangling surface intersects the boundary. We show that there are universal logarithmic boundary terms in the entanglement R\'{e}nyi entropy and derive them for different conformal field theories and geometrical configurations. The paper covers such topics as spectral geometry on manifolds with conical singularities crossing the boundaries, the dependence of the entanglement entropy on mutual position of the boundary and the entangling surface, effects of acceleration and rotation of the boundary, relations of coefficients in the trace anomaly to coefficients in the boundary logarithmic terms in the entropy. The computations are done for scalar, spinor and gauge fields.