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TT: Fachverband Tiefe Temperaturen

TT 87: Frustrated Magnets: Spin Liquids

TT 87.14: Talk

Friday, March 22, 2024, 13:00–13:15, H 3010

Treating anyonic statistics within a full hypergraph decomposition — •Matthias Mühlhauser, Viktor Kott, and Kai Phillip Schmidt — Friedrich-Alexander-Universität Erlangen-Nürnberg

We describe how to execute a full hypergraph decomposition[1] to set up a linked-cluster expansion for the topological phase of Kitaev’s Toric Code in a uniform magnetic field. An important challenge for such an expansion is to correctly incorporate the non-local anyonic braiding statistics into the calculations on the clusters. Indeed, the anyonic statistics lead to counter-intuitive effects like clusters which contribute to irreducible one-quasiparticle matrix elements despite hosting no excitation. We explain how to incorporate the non-local statistics within hypergraph expansions for perturbative series expansions of the one-charge gap, the one-flux gap, and the ground-state energy in the thermodynamic limit.

[1] Phys. Rev. E 105, 064110

Keywords: Toric Code; Anyon; Linked Cluster; Hypergraph; Graph