Spin Drude weight for the integrable XXZ chain with arbitrary spin

Using generalized hydrodynamics (GHD), we exactly evaluate the finite-temperature spin Drude weight at zero magnetic field for the integrable XXZ chain with arbitrary spin and easy-plane anisotropy. First, we construct the fusion hierarchy of the quantum transfer matrices ($T$-functions) and derive functional relations ($T$- and $Y$-systems) satisfied by the $T$-functions and certain combinations of them ($Y$-functions). Through analytical arguments, the $Y$-system is reduced to a set of non-linear integral equations, equivalent to the thermodynamic Bethe ansatz (TBA) equations. Then, employing GHD, we calculate the spin Drude weight at arbitrary finite temperatures. As a result, a characteristic fractal-like structure of the Drude weight is observed at arbitrary spin, similar to the spin-1/2 case. In our approach, the solutions to the TBA equations (i.e., the $Y$-functions) can be explicitly written in terms of the $T$-functions, thus allowing for a systematic calculation of the high-temperature limit of the Drude weight.