Finite-temperature transport in disordered Heisenberg chains

Using numerical diagonalization techniques, we explore the effect of local and bond disorder on the finite-temperature spin and thermal conductivities of the one-dimensional anisotropic spin-1/2 Heisenberg model. High-temperature results for local disorder show that the dc conductivities are finite, apart from the uncorrelated $XY$ case where dc transport vanishes. Moreover, at strong disorder, we find finite dc conductivities at all temperatures $T$ except at $T=0$. The low-frequency conductivities are characterized by a nonanalytic cusp shape. Similar behavior is found for bond disorder.

Figure 1

(Color online) Dynamical spin conductivity $\sigma \left(\omega \right)$ at $T\to \infty$ for local disorder $W=2$ and various $\Delta$ (curves normalized to unity) evaluated via ED $\left(L=14\right)$ and for $\Delta =1$ also via MCLM $\left(L=24\right)$.

Figure 2

(Color online) Dynamical thermal conductivity $\kappa \left(\omega \right)$ at $T\to \infty$ for $W=2$ and various $\Delta$ (curves normalized to unity) evaluated via ED $\left(L=14\right)$ and MCLM $\left(L=24\right)$.

Figure 3

(Color online) Spin conductivity $\sigma \left(\omega \right)$ for $\Delta =1$ and $W=2$ for various $T$.

Figure 4

(Color online) Thermal conductivity $\kappa \left(\omega \right)$ for $\Delta =1$ and $W=2$ for various $T$.

Figure 5

(Color online) $T\to \infty$ results for $\sigma \left(\omega \right)$ and for $\Delta =1$ and different disorder $W$ (curves are normalized).

Figure 6

(Color online) $T\to \infty$ results for $\kappa \left(\omega \right)$ for $\Delta =1$ and different $W$ (curves are normalized).