Heat conductivity of the Heisenberg spin-1/2 ladder: From weak to strong breaking of integrability

Abstract

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.

5 pages, 5 figures (+ 5 pages, 8 figures), accepted for publication in Physical Review Letters

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