Bulk-to-boundary anyon fusion from microscopic models
- URL: http://arxiv.org/abs/2302.01835v1
- Date: Fri, 3 Feb 2023 16:20:36 GMT
- Title: Bulk-to-boundary anyon fusion from microscopic models
- Authors: Julio C. Magdalena de la Fuente, Jens Eisert, Andreas Bauer
- Abstract summary: We study the fusion events between anyons in the bulk and at the boundary in fixed-point models of 2+1-dimensional non-chiral topological order.
A recurring theme in our construction is an isomorphism relating twisted cohomology groups to untwisted ones.
The results of this work can directly be applied to study logical operators in two-dimensional topological error correcting codes with boundaries described by a twisted gauge theory of a finite group.
- Score: 2.025761610861237
- License: http://creativecommons.org/licenses/by-sa/4.0/
- Abstract: Topological quantum error correction based on the manipulation of the anyonic
defects constitutes one of the most promising frameworks towards realizing
fault-tolerant quantum devices. Hence, it is crucial to understand how these
defects interact with external defects such as boundaries or domain walls.
Motivated by this line of thought, in this work, we study the fusion events
between anyons in the bulk and at the boundary in fixed-point models of
2+1-dimensional non-chiral topological order defined by arbitrary fusion
categories. Our construction uses generalized tube algebra techniques to
construct a bi-representation of bulk and boundary defects. We explicitly
derive a formula to calculate the fusion multiplicities of a bulk-to-boundary
fusion event for twisted quantum double models and calculate some exemplary
fusion events for Abelian models and the (twisted) quantum double model of S3,
the simplest non-Abelian group-theoretical model. Moreover, we use the folding
trick to study the anyonic behavior at non-trivial domain walls between twisted
S3 and twisted Z2 as well as Z3 models. A recurring theme in our construction
is an isomorphism relating twisted cohomology groups to untwisted ones. The
results of this work can directly be applied to study logical operators in
two-dimensional topological error correcting codes with boundaries described by
a twisted gauge theory of a finite group.
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