Analytical results for the low-temperature Drude weight of the XXZ spin chain

The spin-1/2 XXZ chain is an integrable lattice model and parts of its spin current can be protected by local conservation laws for anisotropies -1 < Delta < 1. In this case, the Drude weight D(T) is nonzero at finite temperatures T. Here we obtain analytical results for D(T) at low temperatures for zero external magnetic field and anisotropies Delta = cos(n pi/m) with n, m coprime integers, using the thermodynamic Bethe ansatz. We show that to leading orders D(T) = D(0) - a(Delta)T2K-2 - b(1)(Delta)T-2 where K is the Luttinger parameter and the prefactor a(Delta), obtained in closed form, has a fractal structure as a function of anisotropy Delta. The prefactor b(1)(Delta), on the other hand, does not have a fractal structure and can be obtained in a standard field-theoretical approach. Including both temperature corrections, we obtain an analytic result for the low-temperature asymptotics of the Drude weight in the entire regime -1 < Delta = cos(pi pi/m) < 1.

Automated summary

The spin-1/2 XXZ chain shows non-zero Drude weight at finite temperatures, with the leading orders of the Drude weight expressed as a fractal structure dependent on anisotropy Delta. The analytical results for low-temperature asymptotics were obtained using a thermodynamic Bethe ansatz approach.