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arXiv · 2401.06507

Incorporating non-local anyonic statistics into a graph decomposition

M. Mühlhauser·V. Kott·K. P. Schmidt
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Abstract

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.

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M. Mühlhauser, V. Kott, K. P. Schmidt. 2024-01-12. Incorporating non-local anyonic statistics into a graph decomposition. https://arxiv.org/abs/2401.06507

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