Thermal drag revisited: Boltzmann versus Kubo

TL;DR

This paper compares Boltzmann and Kubo formalisms for calculating phonon-spin drag effects on thermal conductivity, showing they agree at leading order and discussing their applicability and extensions.

Contribution

It provides a unified derivation of the drag thermal conductivity using both approaches and explores their validity and generalizations.

Findings

Boltzmann and Kubo approaches yield identical results at leading order.

The derived expressions are applicable to fermionic excitations and anomalous couplings.

The paper highlights regimes relevant to real materials.

Abstract

The effect of mutual drag between phonons and spin excitations on the thermal conductivity of a quantum spin system is discussed. We derive general expression for the drag component of the thermal current using both Boltzmann equation approach and Kubo linear-response formalism to leading order in the spin-phonon coupling. We demonstrate that aside from higher-order corrections which appear in the Kubo formalism both approaches yield identical results for the drag thermal conductivity. We discuss the range of applicability of our result and provide a generalization of our consideration to the cases of fermionic excitations and to anomalous forms of boson-phonon coupling. Several asymptotic regimes of our findings relevant to realistic situations are highlighted.