Entanglement entropy of skeletal regions

Entanglement entropy (EE) provides deep insights about quantum matter. For most groundstates and spatial regions, the EE is dominated by the celebrated area law. However, much less is known about the EE of skeletal regions, i.e. regions without volume such as a line embedded in 2D. When the boundary and volume coincide, there is little understanding about what is encoded in the EE. Here, we study this question using a 2D harmonic lattice model that leads to a relativistic massless scalar (conformal field theory) at low energy. We find new universal contributions to the EE as a function of the geometry of the skeletal region. We also discuss the field theory interpretation, and outline general open questions.