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

## TL;DR

This paper derives an exact expression for thermal conductance in spin-boson systems near equilibrium, revealing a power-law temperature dependence and validating predictions with quantum Monte Carlo simulations.

## Contribution

It provides a systematic derivation of thermal conductance near equilibrium and confirms the power-law behavior through numerical simulations, clarifying the transport mechanism.

## Key findings

- Thermal conductance follows a power-law $ imes T^{2s+1}$ at low temperatures.
- Quantum Monte Carlo confirms the theoretical predictions across various baths.
- Noninteracting-blip approximation accurately describes incoherent transport.

## 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 $\propto T^{2s+1}$ 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.