Incoherent transport induced by a single static impurity in a Heisenberg chain

The effect of a single static impurity on the many-body states and on the spin and thermal transport in the one-dimensional anisotropic Heisenberg chain at finite temperatures is studied. Whereas the pure Heisenberg model reveals Poisson level statistics and dissipationless transport due to integrability, we show using the numerical approach that a single impurity induces Wigner-Dyson level statistics and at high enough temperature incoherent transport within the chain, whereby the relaxation time and dc conductivity scale linearly with length.

Figure 1

(Color online) Parameter $\eta$ for the deviation from the WD level distribution vs impurity field $b_0$ for $\Delta =0.8$ and various $L$.

Figure 2

(Color online) Level-fluctuation parameter ${\Delta }_3\left(N\right)$ for fixed $\Delta =0.8$ and $b_0=0.8$ and different system length $L$. For comparison the RMT result is presented (dotted line).

Figure 3

(Color online) High-$T$ spin stiffness $D/\beta$ vs $1/L$.

Figure 4

(Color online) (a) High-$T$ results for scaled thermal conductivity ${\kappa }^{\prime }/L$ vs $L\omega$ for $\Delta =0.5$ and $b_0=0.5$ as calculated for different $L=16–24$. (b) Extracted scaled memory function $L{N}^{″}\left(\omega \right)$. Perturbation-theory result is also plotted (dashed curve). (c) $N^{″}\left(\omega \right)/b_0^2$ for different impurity fields $b_0=0.4–0.6$ with $\Delta =0.5$ and $L=24$.

Figure 5

(Color online) (a) Scaled spin conductivity ${\sigma }^{\prime }/L$ vs $L\omega$ for different $L=16–24$, and (b) corresponding $M^{″}\left(\omega \right)$.