Ballistic transport in integrable quantum lattice models with degenerate spectra

We study ballistic transport in integrable quantum lattice models, i.e., in the spin XXZ and Hubbard chains, close to the noninteracting limit. It is by now well established that the stiffnesses of spin and charge currents reveal, at high temperatures, a discontinuous reduction (jump) when the interaction is introduced. We show that the jumps are related to the large degeneracy of the parent noninteracting models and, more generally, can appear in other integrable models with macroscopic degeneracies. These degeneracies are properly captured by the degenerate perturbation calculations which may be performed for large systems. We find that the discontinuities and the quasilocality of the conserved current in this limit can be traced back to the nonlocal character of an effective interaction. From the latter observation we identify a class of observables which show discontinuities.