Unified contact-free formulation of linear-response transport theory
Abstract
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.
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BibTeX
@misc{wang2026unified,
title = {{Unified contact-free formulation of linear-response transport theory}},
author = {Ziqian Wang and Ji Feng},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.15371},
eprint = {2609.15371},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.15371},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Unified contact-free formulation of linear-response transport theory
AU - Ziqian Wang
AU - Ji Feng
PY - 2026
DA - 2026/09/14
PB - arXiv
DO - 10.48550/arxiv.2609.15371
UR - https://arxiv.org/abs/2609.15371
AB - 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.
ER -