Nonballistic heat conduction in an integrable random-exchange Ising chain studied with quantum master equations

Abstract

We numerically investigate the heat conduction in a random-exchange Ising spin chain by using the quantum master equation. The chain is subject to a uniform transverse field $h$, while the exchange couplings ${{Q}_{n}}$ between the nearest neighbor spins are random; the largest size we simulate is up to 10. This model is integrable; i.e., the nearest neighbor level spacing distribution is Poissonian. However, we find clear evidence of nonballistic transport. In the small coupling regime $({Q}_{n}\ensuremath{\ll}h)$, an energy and/or temperature gradient in the bulk of the system is observed and the energy current appears to be proportional to the inverse of the system size. Moreover, we find that in the low and high temperature regimes, the thermal conductivity $\ensuremath{\kappa}$ and the specific heat ${C}_{v}$ have the same dependence on temperature. The large coupling case $({Q}_{n}\ensuremath{\sim}h)$ is also discussed.