# Analytic calculation of the vison gap in the Kitaev spin liquid

## TL;DR

This paper derives an analytical expression for the vison gap in the Kitaev spin liquid by calculating the phase shift of Majorana fermions scattering off a bond-flip, providing a precise value and potential for broader lattice applications.

## Contribution

It introduces an analytical method to compute the vison gap in the Kitaev spin liquid, improving upon previous numerical approaches.

## Key findings

- Analytical expression for the vison gap: Δ = 0.2633J
- Phase shift calculation for Majorana fermions
- Applicability to complex lattices like the hyper-octagonal lattice

## Abstract

Although the ground-state energy of the Kitaev spin liquid can be calculated exactly, the associated vison gap energy has to date only been calculated numerically from finite size diagonalization. Here we show that the phase shift for scattering Majorana fermions off a single bond-flip can be calculated analytically, leading to a closed-form expression for the vison gap energy $\Delta = 0.2633J$. Generalizations of our approach can be applied to Kitaev spin liquids on more complex lattices such as the three dimensional hyper-octagonal lattice.