  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.

Strongly Correlated Electrons