Heat Conductivity of the Heisenberg Spin-1/2 Ladder: From Weak to Strong Breaking of Integrability.

We investigate the heat conductivity κ of the Heisenberg spin-1/2 ladder at finite temperature covering the entire range of interchain coupling J(⊥), by using several numerical methods and perturbation theory within the framework of linear response. We unveil that a perturbative prediction κ∝J(⊥)(-2), based on simple golden-rule arguments and valid in the strict limit J(⊥)→0, applies to a remarkably wide range of J(⊥), qualitatively and quantitatively. In the large J(⊥) limit, we show power-law scaling of opposite nature, namely, κ∝J(⊥)(2). Moreover, we demonstrate the weak and strong coupling regimes to be connected by a broad minimum, slightly below the isotropic point at J(⊥)=J(∥). Reducing temperature T, starting from T=∞, this minimum scales as κ∝T(-2) down to T on the order of the exchange coupling constant. These results provide for a comprehensive picture of κ(J(⊥),T) of spin ladders.