Incorporating non-local anyonic statistics into a graph decomposition

In this work we describe how to systematically implement a full graph decomposition to set up a linked-cluster expansion for the topological phase of Kitaev’s toric code in a field. This demands to include the non-local effects mediated by the mutual anyonic statistics of elementary charge and flux...

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Bibliographic Details
Published inSciPost physics core Vol. 7; no. 2; p. 031
Main Authors Mühlhauser, Matthias, Kott, Viktor, Schmidt, Kai Phillip
Format Journal Article
LanguageEnglish
Published SciPost 30.05.2024
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Summary:In this work we describe how to systematically implement a full graph decomposition to set up a linked-cluster expansion for the topological phase of Kitaev’s toric code in a field. This demands to include the non-local effects mediated by the mutual anyonic statistics of elementary charge and flux excitations. Technically, we describe how to consistently integrate such non-local effects into a hypergraph decomposition for single excitations. The approach is demonstrated for the ground-state energy and the elementary excitation energies of charges and fluxes in the perturbed topological phase.
ISSN:2666-9366
2666-9366
DOI:10.21468/SciPostPhysCore.7.2.031