Abstract
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.
Highlights
We revisit the problem of boundary excitations at a topological boundary or junction defects between topological boundaries in nonchiral bosonic topological orders in 2 þ 1 dimensions
These objects are intimately related to topological defect lines in conformal field theories (CFT’s), which have been extensively studied e.g., in [6,7,8,9,10,11,12]
Topological orders have found applications in quantum computing, given their robustness against decoherence, and it has been proposed in the literature that topological defects might be a more convenient candidate to realize universal computing [13]
Summary
We revisit the problem of boundary excitations at a topological boundary or junction defects between topological boundaries in nonchiral bosonic topological orders in 2 þ 1 dimensions. Gapped boundaries can be described by anyon condensation [1,3,15,16,17,18,19,20,21,22]. For a given nonchiral bulk phase B in 2 þ 1 dimensions, there could be multiple different gapped boundaries, each characterized by a distinct pattern of anyon condensation.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
