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arXiv · 2206.05762

$\mathbb{Z}_2$ topologically ordered phases on a simple hyperbolic lattice

Hiromi Ebisu·Bo Han
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Abstract

In this work, we consider 2D $\mathbb{Z}_2$ topologically ordered phases ($\mathbb{Z}_2$ toric code and the modified surface code) on a simple hyperbolic lattice. Introducing a 2D lattice consisting of the product of a 1D Cayley tree and a 1D conventional lattice, we investigate two topological quantities of the $\mathbb{Z}_2$ topologically ordered phases on this lattice: the ground state degeneracy on a closed surface and the topological entanglement entropy. We find that both quantities depend on the number of branches and the generation of the Cayley tree. We attribute these results to a huge number of superselection sectors of anyons.

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Hiromi Ebisu, Bo Han. 2022-06-12. $\mathbb{Z}_2$ topologically ordered phases on a simple hyperbolic lattice. https://doi.org/10.1103/physrevresearch.4.04309

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