Non-linear Transport by Bethe Bound States

We consider non-linear ballistic spin transport in the XXZ spin chain and derive an analytical result for the non-linear Drude weight $D^{(3)}$ at infinite temperatures. In contrast to the linear Drude weight $D^{(1)}$, we find that the result not only depends on anisotropy but also on the string length of the quasiparticles transporting the spin current. Our result provides further insights into transport by quasiparticles and raises questions about Luttinger liquid universality.