Level statistics of the strained Kitaev honeycomb model with Heisenberg interactions and disorder

We study the Kitaev honeycomb spin model in the presence of geometric strain and weak residual Heisenberg interactions. Similarly to graphene, as triaxial strain is applied, flat bands appear resembling Landau levels for the Majorana fermions. It is known that weak Heisenberg interactions that don't take you out of the ground state flux sector lead to an effective interaction term between the Majoranas.

We argue that the effective interaction has a bipartite structure (γ^Aγ^Aγ^Bγ^B). Further, in the presence of a disordered lattice the interaction is effectively random.

We show that a majorana model with random interaction of the above mentioned type leads to level statistics similar to the Sachdev-Ye-Kitaev (SYK) model, but with a reduced symmetry.
However, we argue that in a realistic system, where Heisenberg interactions can be long ranged, weak SYK-type interactions (γγγγ) will appear. Further we show by scaling analysis that in the thermodynamic limit any amount of SYK-type interactions will cause the level statistics to flow to that of the pure SYK model.