Ballistic transport in integrable quantum lattice models with degenerate spectra

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