Spin and thermal conductivity in a classical disordered spin chain

The transport quantities of a classical spin chain with quenched disorder in antiferromagnetic coupling $J_i$ are evaluated using a dynamical simulation at finite temperatures $T>0$. Since the classical model is nonintegrable, spin and thermal conductivities remain finite even in the pure case. On the other hand, the role of disorder becomes crucial at low $T$, leading to a vanishing transport due to Anderson localization within the linearized regime. The crossover from the insulator to the conductor appears both for spin and thermal transport at quite low $T^{*}\ll J$. Still the many-body localization regime at $T>0$ evidenced by extremely short mean free paths can be strongly enhanced by introducing into the model an additional staggered field.

Figure 1

Temperature dependence of renormalized (a) spin conductivity ${\tilde{\sigma }}_s=T{\sigma }_s$ and (b) thermal conductivity $\tilde{\kappa }=T^2\kappa$ for various disorders $\delta J=0$–$0.8$.

Figure 2

An example of local spin deviations emerging from the linearized Eq. (2) in the case of $\delta J=0.8$ and $T\sim 0.02$.

Figure 3

Specific heat $C_V$ and uniform susceptibility ${\chi }_s$ vs $T$ for the pure case $\delta J=0$ and different values of the staggered field $B$.

Figure 4

Transport mean free paths vs $T$: (a) spin diffusion $l_s\left(T\right)$, (b) the thermal $l_t\left(T\right)$, and (c) the Wiedemann-Franz ratio $W=l_t/l_s$ for different disorder strength $\delta J=0$–$0.8$ and $B=0$. Note the log scale.

Figure 5

Transport mean free paths vs $T$: (a) spin diffusion $l_s\left(T\right)$, (b) thermal $l_t\left(T\right)$, and (c) the ratio $W=l_t/l_s$ for different staggered fields $B=0$–$0.5$ and fixed disorder $\delta J=0.4$.