Anomalous Thermal Conductivity of Frustrated Heisenberg Spin Chains and Ladders

We study the thermal transport properties of several quantum-spin chains and ladders. We find indications for a diverging thermal conductivity at finite temperatures for the models examined. The temperature at which the nondiverging prefactor ${\kappa }^{(\mathrm{t}\mathrm{h})}(T)$ peaks is, in general, substantially lower than the temperature at which the corresponding specific heat $c_V(T)$ is maximal. We show that this result of the microscopic approach leads to a substantial reduction for estimates of the magnetic mean-free path $\lambda$ extracted by analyzing recent experiments, as compared to similar analyses by phenomenological theories.

Figure 1

${\kappa }^{(\mathrm{t}\mathrm{h})}$, as defined by Eq. (2), for the Heisenberg chain as a function of temperature. Inset: Data for $L=5–14$, in comparison with the Bethe ansatz result [10] (full line). Main panel: Results using Eq. (5), with $L_{\mathrm{e}\mathrm{f}\mathrm{f}}=(L_0+L_1)/2$. We note that the position of the maximum in ${\kappa }^{(\mathrm{t}\mathrm{h})}$ can be determined confidently with the averaging procedure.

Figure 2

Temperature dependence of ${\kappa }^{(\mathrm{t}\mathrm{h})}$ and the dimensionless specific heat for ladders with twisted boundary conditions and $J_{\perp }=2J_{\parallel }$. Both magnitudes are computed using the average procedure (5) described in the text. The specific heat for a $2\times 100$-ladder computed with QMC is plotted for comparison (squares). Inset ${\kappa }^{(\mathrm{t}\mathrm{h})}$ for $L=3$, 5, 7 (from bottom up) and $L=4$, 6 (from top down) in the low-temperature region.

Figure 3

${\kappa }^{(\mathrm{t}\mathrm{h})}$ and dimensionless specific heat for the frustrated Heisenberg chain with $\alpha =0.35$ and different lattice sizes $L=8$, 10, 12, 14, the arrows indicate increasing $L$, compare 9. Inset : Finite size analysis ($L=6–14$) of the high temperature residue $C(L)$ defined as ${\kappa }^{(\mathrm{t}\mathrm{h})}=C(L)/T^2$ at $T\gg J$ for different values of $\alpha$.

Figure 4

$\tau (T)$ (right scale) and $\lambda (T)$ (left scale) for $\mathrm{C}{\mathrm{a}}_{\mathrm{9}}\mathrm{L}{\mathrm{a}}_{\mathrm{5}}\mathrm{C}{\mathrm{u}}_{\mathrm{24}}{\mathrm{O}}_{\mathrm{41}}$ extracted using Eq. (6). The experimental data by Hess et al. [7] is shown in the inset (filled circles) together with an analytic fit (solid line) discussed in the text.