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 (µ = 0). These disagreements do not arise from the GHD framework itself but rather from differing treatments of the model's global symmetry at theh=μ=0point, wherehis the magnetic field. Specifically, the controversy concerns whether finite-temperature charge transport atµ = 0 is anomalous superdiffusive, as predicted using GHD when only theSU(2) × SU(2) symmetries are considered, or instead normal diffusive, as found when employing a representation that fully accounts for the model's global [SU(2) × SU(2) × U(1)]/Z22symmetry ath=μ=0. 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-1/2XXXchain ath = 0 and the 1D Hubbard model ath=μ=0. We then reviewT > 0 transport results in gapped 1D integrable models, focusing on charge transport in the 1D Hubbard model ath=μ=0and spin transport in the spin-1/2XXZchain ath = 0 with anisotropyΔ>1. We identify and discuss the origin of the aforementioned discrepancies, showing how their resolution leads to a deeper understanding of anomalous superdiffusion.