Unified contact-free formulation of linear-response transport theory

RESUMO

Thermal Hall transport is conventionally formulated as a current--current Kubo response supplemented by an energy-magnetization correction obtained through an auxiliary pseudogravitational magnetic field. Motivated by this structure, we develop a unified contact-free moment formulation of linear response to scalar sources. For channels whose source contributions vanish in the dc limit, the transport coefficient is the low-frequency residue of a retarded moment--moment correlator, with equal-time endpoint contributions incorporated before the dc limit is taken. The formulation uses only scalar sources, requires no separate magnetization subtraction, is independent of the local-current gauge, and is invariant under admissible redistributions of bond or interaction energy. It organizes particle, grand-energy, and specified spin-density channels within a common source--moment response matrix. Quadratic Landau--Lifshitz spin waves illustrate the method: the secular growth of polarization-moment correlations isolates the finite Hall residue and yields the magnon thermal Hall and spin Nernst coefficients from the same paraunitary band geometry. The formulation provides a unified operator framework that simplifies the organization of particle, thermal, and spin transport and can streamline calculations by eliminating separate contact and magnetization corrections.