I've been reading about frustrated quantum magnets lately and a prominent topic is the study of antiferromagnets on the Kagome lattice. A calculation of the spectrum for the sort of model I have in mind is presented in figure 1 (a) of this paper. The spectrum of the theory is very interesting, partly because there are often dispersionless bands, which is obviously odd. I want to know about a more banal part of the spectrum which I haven't seen discussed elsewhere: the linear band crossings of the top two bands at the $K$ point.
These band crossings look like they could be a sign of some kind of topological non-triviality, like Dirac or Weyl points. However I haven't found any references discussing the nature of these gapless points, and it's also possible that they are just protected by some kind of symmetry. Either way, I would like to understand the nature of those gapless points, so if someone is aware of the origin of this degeneracy a discussion or reference on them would be very helpful. Thanks!