Intermediate-temperature dynamics of one-dimensional Heisenberg antiferromagnets

We present a general theory for the intermediate-temperature (T) properties of Heisenberg antiferromagnets of spin-$S$ ions on p-leg ladders, valid for $2Sp$ even or odd. Following an earlier proposal for $2Sp$ even [Damle and Sachdev, Phys. Rev. B 57, 8307 (1998)], we argue that an integrable, classical, continuum model of a fixed-length, three-vector applies over an intermediate-temperature range; this range becomes very wide for moderate and large values of $2Sp.$ The coupling constants of the effective model are known exactly in terms of the energy gap above the ground state $\Delta$ (for $2Sp$ even), or a crossover scale $T_0$ (for $2Sp$ odd). Analytic and numeric results for dynamic and transport properties are obtained, including some exact results for the spin-wave damping. Numerous quantitative predictions for neutron scattering and NMR experiments are made. A general discussion on the nature of $T>\mathrm{}0\mathrm{}$ transport in integrable systems is also presented: an exact solution of a toy model proves that diffusion can exist in integrable systems, provided proper care is taken in approaching the thermodynamic limit.