Heat transport via a local two-state system near thermal equilibrium

Heat transport in spin-boson systems near the thermal equilibrium is systematically investigated. An asymptotically exact expression for the thermal conductance in a low-temperature regime wherein transport is described via a co-tunneling mechanism is derived. This formula predicts the power-law temperature dependence of thermal conductance $\propto T^{2s+1}$ for a thermal environment of spectral density with the exponent $s$. An accurate numerical simulation is performed using the quantum Monte Carlo method, and these predictions are confirmed for arbitrary thermal baths. Our numerical calculation classifies the transport mechanism, and shows that the noninteracting-blip approximation quantitatively describes thermal conductance in the incoherent transport regime.