Non-dissipative thermal transport in the massive regimes of the XXZ chain

We present exact results on the thermal conductivity of the one-dimensional spin-1/2 XXZ model in the massive antiferromagnetic and ferromagnetic regimes. The thermal Drude weight is calculated by a lattice path integral formulation. Numerical results for wide ranges of temperature and anisotropy as well as analytical results in the low- and high-temperature limits are presented. At finite temperature, the thermal Drude weight is finite and hence there is non-dissipative thermal transport even in the massive regime. At low temperature, the thermal Drude weight behaves as D-th(T) similar to exp(-delta/T)/rootT where delta is the one-spinon (respectively one-magnon) excitation energy for the antiferromagnetic (respectively ferromagnetic) regime.