Boundary effects in entanglement entropy

Understand

We present a number of explicit calculations of Renyi and entanglement entropies in situations where the entangling surface intersects the boundary in $d$-dimensional Minkowski spacetime.

• When the boundary is a single plane we compute the contribution to the entropy due to this intersection, first in the case of the Neumann and Dirichlet boundary conditions, and then in the case of a generic Robin type boundary condition.
• The flow in the boundary coupling between the Neumann and Dirichlet phases is analyzed in arbitrary dimension $d$ and is shown to be monotonic, the peculiarity of $d=3$ case is noted.
• We argue that the translational symmetry along the entangling surface is broken due the presence of the boundary which reveals that the entanglement is not homogeneous.