Entanglement in the vertex state: conformal interface approach

The multipartite entanglement structure for the ground states of two dimensional topological phases is an interesting albeit not well understood question. Utilizing the bulk-boundary correspondence, the tripartite entanglement calculation of 2d topological phases can be reduced to that on the vertex state, defined by the boundary conditions at the interfaces between spatial regions. We use the conformal interface technique to calculate the entanglement measures of the vertex state, which include the area-law, geometrical and topological pieces, and the possible extra order one contribution. A direct consequence is the Markov gap $h=c/3log{2}$, which applies to the vertex state of general rational conformal field theory. Finally, we support our prediction by numerical evidence in the n-vertex state of real fermion (boundary of chiral superconductor).