Composing topological domain walls and anyon mobility

• URL: http://arxiv.org/abs/2208.14018v1
• Date: Tue, 30 Aug 2022 06:47:04 GMT
• Title: Composing topological domain walls and anyon mobility
• Authors: Peter Huston, Fiona Burnell, Corey Jones, David Penneys
• Abstract summary: Topological domain walls separating 2+1 dimensional topologically ordered phases can be understood in terms of Witt equivalences. We develop a framework for computing the decomposition of parallel domain walls into indecomposable superselection sectors.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

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