Multipartitioning topological phases by vertex states and quantum entanglement

Understand

We discuss multipartitions of the gapped ground states of (2+1)-dimensional topological liquids into three (or more) spatial regions that are adjacent to each other and meet at points.

• By considering the reduced density matrix obtained by tracing over a subset of the regions, we compute various correlation measures, such as entanglement negativity, reflected entropy, and associated spectra.
• We utilize the bulk-boundary correspondence to show that such multipartitions can be achieved by using what we call vertex states in (1+1)-dimensional conformal field theory -- these are a type of state used to define an interaction vertex in string field theory and can be thought of as a proper generalization of conformal boundary states.
• This approach allows an explicit construction of the reduced density matrix near the entangling boundaries.