We revisit the problem of boundary excitations at a topological boundary or junction defects between topological boundaries in nonchiral bosonic topological orders in $2+1$ dimensions. Based on physical considerations, we derive a formula that relates the fusion rules of the boundary excitations and the “half-linking” number between condensed anyons and confined boundary excitations. This formula is a direct analogue of the Verlinde formula. We also demonstrate how these half-linking numbers can be computed in explicit Abelian and non-Abelian examples. As a fundamental property of topological orders and their allowed boundaries, this should also find applications in the search for suitable platforms realizing quantum computing devices.

• Received 20 February 2019

DOI:https://doi.org/10.1103/PhysRevLett.123.051602

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Funded by SCOAP³.

Published by the American Physical Society