Composing topological domain walls and anyon mobility
Peter Huston, Fiona Burnell, Corey Jones, David Penneys
SciPost Phys. 15, 076 (2023) · published 4 September 2023
- doi: 10.21468/SciPostPhys.15.3.076
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Abstract
Topological domain walls separating 2+1 dimensional topologically ordered phases can be understood in terms of Witt equivalences between the UMTCs describing anyons in the bulk topological orders. However, this picture does not provide a framework for decomposing stacks of multiple domain walls into superselection sectors — i.e., into fundamental domain wall types that cannot be mixed by any local operators. Such a decomposition can be understood using an alternate framework in the case that the topological order is anomaly-free, in the sense that it can be realized by a commuting projector lattice model. By placing these Witt equivalences in the context of a 3-category of potentially anomalous (2+1)D topological orders, we develop a framework for computing the decomposition of parallel topological domain walls into indecomposable superselection sectors, extending the previous understanding to topological orders with non-trivial anomaly. We characterize the superselection sectors in terms of domain wall particle mobility, which we formalize in terms of tunnelling operators. The mathematical model for the 3-category of topological orders is the 3-category of fusion categories enriched over a fixed unitary modular tensor category.
Cited by 4
Authors / Affiliations: mappings to Contributors and Organizations
See all Organizations.- 1 Peter Huston,
- 2 Fiona Burnell,
- 3 Corey Jones,
- 4 David Penneys
- 1 Vanderbilt University
- 2 University of Minnesota
- 3 North Carolina State University [NCSU]
- 4 The Ohio State University [OSU]