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

Analytic calculation of the vison gap in the Kitaev spin liquid