AI 中文总结
提出一种统一的线性响应输运理论无接触矩公式，仅用标量源，无需磁化修正，适用于粒子、热和自旋输运，并以朗道-利夫希茨自旋波验证了热霍尔和自旋能斯特系数的计算。
AI 中文摘要
热霍尔输运通常被表述为电流-电流久保响应，并辅以通过辅助赝引力磁场获得的能量磁化修正。受此结构启发，我们发展了一种针对标量源的统一无接触矩公式。对于在直流极限下源贡献消失的通道，输运系数是延迟矩-矩关联函数的低频留数，其中等时端点贡献在取直流极限之前被纳入。该公式仅使用标量源，无需单独的磁化扣除，独立于局域电流规范，并且在键能或相互作用能的允许重分配下保持不变。它将粒子、总能量和特定自旋密度通道组织在一个共同的源-矩响应矩阵中。二次朗道-利夫希茨自旋波说明了该方法：极化矩关联的长期增长分离出有限的霍尔留数，并从相同的幺正带几何中得出磁振子热霍尔和自旋能斯特系数。该公式提供了一个统一的算符框架，简化了粒子、热和自旋输运的组织，并通过消除单独的接触和磁化修正来简化计算。
英文摘要
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.
Comments10 pages, no figures
