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

Abstract

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