What do we know about a quantum phase transition from a gapless spin liquid to a gapped topological spin liquid? Is there any model to realize such a transiton? Thanks!
Indeed, the Kitaev model is some two-dimensional spin model on the honeycomb lattice. For some regime in parameter space, the ground state is a gapped spin liquid (in fact it is in the same phase as the toric code). By tuning the parameters, one encounters a second order phase transition and one then enters a gapless spin liquid, characterized by a dirac cone as its low energy theory. (More exactly: the fractional excitations consist of two gapless Majorana cones and localized gapped fluxes.)
Here is Kitaev's beauty: https://arxiv.org/abs/cond-mat/0506438