Dynamical separation of charge and energy transport in one-dimensional Mott insulators

One-dimensional Mott insulators can be described using the sine-Gordon model, an integrable quantum field theory that provides the low-energy effective description of several one-dimensional gapped condensed matter systems, including recent realizations with trapped ultra-cold atoms. Employing the theory of Generalized Hydrodynamics, we demonstrate that this model exhibits separation of the transport of topological charge vs. energy. Analysis of the quasiparticle dynamics reveals that the mechanism behind the separation is the reflective scattering between topologically charged kinks/antikinks. The effect of these scattering events is most pronounced at strong coupling and low temperatures, where the distribution of quasiparticles is narrow compared to the reflective scattering amplitude. This effect results in a distinctively shaped "arrowhead" light cone for the topological charge.