I will discuss general results regarding the effect of phonons coupled to other degrees of freedom on the thermal conductivity, both obtained within a hydrodynamic approach, as well as through a calculation of the phonon Hall viscosity, and show specific examples in magnets. I will also present some general results for all components of the thermal conductivity tensor in magnets, especially useful in regimes where the current is not carried by well-defined quasiparticles. This includes, but is not limited to, high temperatures as compared with the magnetic exchange scale, which is most easily accessible in magnets.
On a different note, if time allows, I will briefly discuss our recent results on a fully-analytical renormalization group approach for twisted bilayer graphene at charge neutrality.
