We investigate the heat conductivity $kappa$ of the Heisenberg spin-1/2 ladder at finite temperature covering the entire range of inter-chain coupling $J_perp$, by using several numerical methods and perturbation theory within the framework of linear
response. We unveil that a perturbative prediction $kappa propto J_perp^{-2}$, based on simple golden-rule arguments and valid in the strict limit $J_perp to 0$, applies to a remarkably wide range of $J_perp$, qualitatively and quantitatively. In the large $J_perp$-limit, we show power-law scaling of opposite nature, namely, $kappa propto J_perp^2$. Moreover, we demonstrate the weak and strong coupling regimes to be connected by a broad minimum, slightly below the isotropic point at $J_perp = J_parallel$. As a function of temperature $T$, this minimum scales as $kappa propto T^{-2}$ down to $T$ on the order of the exchange coupling constant. These results provide for a comprehensive picture of $kappa(J_perp,T)$ of spin ladders.
We study the thermal transport of a spin-1/2 two leg antiferromagnetic ladder in the direction of legs. The possible effect of spin-orbit coupling and crystalline electric field are investigated in terms of anisotropies in the Heisenberg interactions
on both leg and rung couplings. The original spin ladder is mapped to a bosonic model via a bond-operator transformation where an infinite hard-core repulsion is imposed to constrain one boson occupation per site. The Greens function approach is applied to obtain the energy spectrum of quasi-particle excitations responsible for thermal transport. The thermal conductivity is found to be monotonically decreasing with temperature due to increased scattering among triplet excitations at higher temperatures. A tiny dependence of thermal transport on the anisotropy in the leg direction at low temperatures is observed in contrast to the strong one on the anisotropy along the rung direction, due to the direct effect of the triplet density. Our results reach asymptotically the ballistic regime of the spin - 1/2 Heisenberg chain and compare favorably well with exact diagonalization data.
