Data generated from calculations in "Gauge Field Dynamics in a Multilayer Kitaev Spin Liquid"

The Kitaev honeycomb model hosts a quantum spin liquid in its ground state, where the excitations are gapless Majorana fermions and static Z2 gauge fluxes called visons. We consider Kitaev models stacked on top of each other, weakly coupled by Heisenberg interaction linear in J⊥. This inter-layer coupling breaks the integrability of the model and makes the gauge fields dynamic. While single visons stay static in this model, an inter-layer pair of visons can hop with a hopping amplitude linear in J⊥, but remains confined to a single plane. An intra-layer vison-pair, in contrast, is constrained to move along the stacking direction only. Depending on the anisotropy of the Kitaev couplings Kx,Ky,Kz, the intra-layer vison pairs show completely different dynamical behaviours. While coherent intra-layer tunnelling is possible for sufficiently strong anisotropies, only incoherent processes are possible in the isotropic case. When a magnetic field opens a gap for Majorana fermions, one can identify two types of intra-layer vison pairs, one bosonic and one fermionic. Only the bosonic pair obtains a hopping rate linear in J⊥. We argue that our results can be used to identify leading instabilities of the Kitaev phase induced by the inter-layer coupling.