Equivalence between vortices, twists and chiral gauge fields in Kitaev's honeycomb lattice model

TL;DR

This paper shows that in Kitaev's honeycomb model, vortices, twists, and chiral gauge fields are equivalent in the continuum limit, enabling new ways to encode Majorana-bound states for potential experimental realization.

Contribution

It establishes the equivalence between vortices, twists, and chiral gauge fields in the model, providing a novel perspective on Majorana defect encoding.

Findings

Chiral gauge fields can be equivalent to $ ext{Z}_2$ gauge fields in the continuum limit.

Majorana-bounding vortices and lattice twists are adiabatically connected.

This equivalence suggests new experimental approaches for Majorana defect encoding.

Abstract

We demonstrate that $\mathbb{Z}_2$ gauge transformations and lattice deformations in Kitaev's honeycomb lattice model can have the same description in the continuum limit of the model in terms of chiral gauge fields. The chiral gauge fields are coupled to the Majorana fermions that satisfy the Dirac dispersion relation in the non-Abelian sector of the model. For particular values, the effective chiral gauge field becomes equivalent to the $\mathbb{Z}_2$ gauge field, enabling us to associate effective fluxes to lattice deformations. Motivated by this equivalence, we consider Majorana-bounding $\pi$ vortices and Majorana-bounding lattice twists and demonstrate that they are adiabatically connected to each other. This equivalence opens the possibility for novel encoding of Majorana-bounding defects that might be easier to realise in experiments.