Finite-temperature transport in gapless and gapped 1D integrable quantum systems

Generalized hydrodynamics (GHD) has successfully addressed several open questions regarding finite-temperature (T > 0) transport in one-dimensional (1D) integrable models, including the mechanisms behind anomalous superdiffusive transport. However, disagreements persist concerning finite-temperature charge transport in the 1D Hubbard model at zero chemical potential. These disagreements do not arise from the GHD framework itself but rather from differing treatments of the model's global symmetry at the zero chemical potential and magnetic field point, Specifically, the controversy concerns whether finite-temperature charge transport at zero chemical potential is anomalous superdiffusive, as predicted using GHD when only the SU(2)xSU(2) symmetries are considered, or instead normal diffusive, as found when employing a representation that fully accounts for the model's global [SU(2)xSU(2)xU(1)]/Z_2^2 symmetry. This work aims to contribute to resolving this issue and advancing the understanding of transport in such systems. We begin by briefly reviewing GHD and other methods predictions regarding anomalous superdiffusive spin transport at finite temperature in gapless 1D integrable models such as the spin-1/2 XXX chain at zero field and the 1D Hubbard model at zero chemical potential. We then review T > 0 transport results in gapped 1D integrable models, focusing on charge transport in the 1D Hubbard model and spin transport in the spin-1/2 XXZ chain at with anisotropy larger than 1. We identify and discuss the origin of the aforementioned discrepancies, showing how their resolution leads to a deeper understanding of anomalous superdiffusion.