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arXiv · 2210.09180

The Kitaev honeycomb model on surfaces of genus $g \geq 2$

John Brennan·Jiří Vala
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Abstract

We present a construction of the Kitaev honeycomb lattice model on an arbitrary higher genus surface. We first generalize the exact solution of the model based on the Jordan-Wigner fermionization to a surface with genus $g = 2$, and then use this as a basic module to extend the solution to lattices of arbitrary genus. We demonstrate our method by calculating the ground states of the model in both the Abelian doubled $\mathbb{Z}_2$ phase and the non-Abelian Ising topological phase on lattices with the genus up to $g = 6$. We verify the expected ground state degeneracy of the system in both topological phases and further illuminate the role of fermionic parity in the Abelian phase.

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John Brennan, Jiří Vala. 2022-10-17. The Kitaev honeycomb model on surfaces of genus $g \geq 2$. https://doi.org/10.1088/1367-2630%2Faabb95

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