The sine-Gordon Drude weight at low temperature

We apply form factor perturbation theory with finite volume regularization to obtain the low-temperature behavior of the Drude weight in the sine-Gordon model. Recent results using Thermodynamic Bethe Ansatz (TBA) indicate that the Drude weight is a complicated function of the coupling reflecting the magnonic structure of the TBA system. In contrast, we find that the leading low-T term in the Drude weight is independent of the sine-Gordon coupling. Our result agrees with the low-T limit of the TBA results of arXiv:2305.15474 at the special "diagonal scattering" points but is larger than those in general. We argue the TBA description fails at general couplings because of its insufficient treatment of nonlocal charges. We show that the form factor perturbation theory is consistent with the Mazur bound when nonlocal charges are taken into account.