Keldysh Theory of Thermal Transport in Multiband Hamiltonians

We establish a comprehensive theoretical framework for systems subjected to astatic uniform temperature gradient, employing the non-equilibriumKeldysh-Dyson formalism. This framework interprets the statistical force due tothe temperature gradient as a mechanical force, utilizing both Luttinger'sscalar and Moreno-Coleman-Tatara's vector potentials, which collectivelyemulate the gauge invariance stemming from the conservation of energy. Ourapproach has the ability to treat heat current and heat magnetization on anequal footing, thereby extending and generalizing previous formalisms. Thederived result for the thermal conductivity is applied to investigate thethermal characteristics of Weyl magnons in a stacked honeycomb ferromagnetfeaturing a trivial insulator phase, a magnon Chern insulator phase, and threeWeyl magnon phases. Against the expectation from the Berry curvature, themagnon Chern insulator phase exhibits the highest transverse thermalconductivity.