Towards topological fixed-point models beyond gappable boundaries

Bauer, Andreas; Eisert, Jens; Wille, Carolin

doi:10.1103/physrevb.106.125143

Cited by 4 publications

(1 citation statement)

References 32 publications

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“…Topological invariance highly restricts the microscopic constituents of these models. In the Turaev-Viro state-sum [7,24], or tensor-network path integrals [5,25] for 2 + 1-dimensional topological order, the topological invariance corresponds to recellulations in a three-dimensional space-time, and the algebraic constraints correspond to the ones defining spherical fusion categories. A different but equivalent picture are Levin-Wen string-net models [2], where recellulations on a two-dimensional space triangulation are represented by linear operators acting on the local degrees of freedom.…”

Section: Models For Topological Phases With Boundarymentioning

confidence: 99%

Bulk-to-boundary anyon fusion from microscopic models

Fuente¹,

Eisert²,

Bauer³

2023

Preprint

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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 nonchiral 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 S 3 , 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 S 3 and twisted Z 2 as well as Z 3 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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Section: Models For Topological Phases With Boundarymentioning

confidence: 99%

Bulk-to-boundary anyon fusion from microscopic models

Fuente¹,

Eisert²,

Bauer³

2023

Preprint

View full text Add to dashboard Cite

show abstract

Bulk-to-boundary anyon fusion from microscopic models

Magdalena de la Fuente,

Eisert,

Bauer

2023

Journal of Mathematical Physics

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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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Disentangling modular Walker-Wang models via fermionic invertible boundaries

Bauer

2023

Phys. Rev. B

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Towards topological fixed-point models beyond gappable boundaries

Cited by 4 publications

References 32 publications

Bulk-to-boundary anyon fusion from microscopic models

Bulk-to-boundary anyon fusion from microscopic models

Bulk-to-boundary anyon fusion from microscopic models

Disentangling modular Walker-Wang models via fermionic invertible boundaries

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