Universal charge and spin Drude weights in one-dimensional Fermi-Hubbard model

Drude weight (DW) is one of the important quantities characterizing the quantum transport properties of many-body systems. Despite of intense studies of many decades, there still lacks rigorous understanding of transport behavior for various quantum phases at low temperatures. In terms of generalised Kohn's formula, here we report on universal properties of DWs in one-dimensional repulsive Fermi-Hubbard model with arbitrary magnetic fields. In addition to the usual charge and spin DWs, we also construct the cross DW that captures the cross influences between the two degrees of freedom in the transport dynamics. We derive analytical expressions of the DWs at different Tomonaga-Luttinger liquid phases, from which general relations between the Luttinger parameters and the DWs are established. We obtain explicit universal critical scaling laws for DWs across various phase boundaries. We propose an experimental protocol to measure the DWs. DWs obtained from a direct numerical simulation of this protocol show good agreement with the analytic results.