Abstract
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 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 non-interacting-blip approximation quantitatively describes thermal conductance in the incoherent transport regime.
Highlights
Heat transport via small systems has recently attracted considerable attention because a lot of intriguing phenomena can emerge reflected from the properties of a system and the surrounding environment
We found that the noninteracting-blip approximation (NIBA) [10] describes thermal conductance in the incoherent tunneling regime accurately
The co-tunneling formula [equation (33)], a new formula that is first derived in the present study, holds universally at low temperatures for an arbitrary exponent, s, as long as the ground state of the system is delocalized (∆eff > 0) In a previous study [30], the thermal conductance in the ohmic case (s = 1) was shown to be proportional to T 3, which is consistent with equation (33), and this T 3-dependence was discussed in terms of the emergence of the Kondo effect
Summary
Heat transport via small systems has recently attracted considerable attention because a lot of intriguing phenomena can emerge reflected from the properties of a system and the surrounding environment. The ohmic environment induces the Kondo effect [25] at sufficiently low temperatures [10, 11, 26, 27] From this background in an equilibrium situation, it is quite natural to ask what happens if one considers heat transport in this system. Two of the present authors (TK and KS) have focused on the transport properties in an ohmic environment and found several Kondo signatures [30], including the T 3-temperature dependence of the thermal conductance. Our formula is asymptotically exact in the co-tunneling transport regime and predicts power-law temperature dependences ∝ T 2s+1 for the thermal environment of spectral density with the exponent s.
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