Transport in almost integrable models: perturbed Heisenberg chains

The heat conductivity kappa(T) of integrable models, like the one-dimensional spin-1/2 nearest-neighbor Heisenberg model, is infinite even at finite temperatures as a consequence of the conservation laws associated with integrability. Small perturbations lead to finite but large transport coefficients which we calculate perturbatively using exact diagonalization and moment expansions. We show that there are two different classes of perturbations. While an interchain coupling of strength J(perpendicular) leads to kappa(T) proportional to 1/J(perpendicular)2 as expected from simple golden-rule arguments, we obtain a much larger kappa(T) proportional to 1/J'4 for a weak next-nearest-neighbor interaction J'. This can be explained by a new approximate conservation law of the J-J' Heisenberg chain.