Determine alternative area spectra for other topological boundary conditions

Determine the spectra of the area operators associated with topological boundary conditions other than the rough boundary condition, including smooth and mixed charge-flux boundary conditions, for the factorization cut of topological tensor networks.

Background

The paper derives the area spectrum for a rough boundary condition, where pure charges condense at the cut. Other topological boundary conditions would change the superselection labels to the anyons that can terminate on the chosen boundary. The authors state that the entropy derivation should remain structurally valid, but the resulting spectra have not been explicitly determined.

References

We leave the explicit determination of these alternative spectra for future work.

Entanglement entropy in topological tensor networks  (2609.10667 - Balasubramanian et al., 9 Sep 2026) in Section 5.2, “The area contribution”