Berry-Landau费米液体理论：存在量子几何时的输运
Berry-Landau Fermi-liquid theory: transport in presence of quantum geometry
- Max Planck Institute for the Physics of Complex Systems（马克斯·普朗克复杂系统物理研究所）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
本文提出Berry-Landau费米液体理论，将量子几何纳入Landau框架，推导出含量子几何贡献的电荷电流，并阐明反常霍尔电导与Drude权重的几何来源。
AI中文摘要：
Landau费米液体理论通过准粒子及其残余相互作用来表征相互作用金属。将非平凡的量子几何——由Berry相位和量子度量编码——作为基本要素纳入其中是一个挑战。我们为跨越费米面的孤立能带中的无自旋费米子构建了Berry-Landau费米液体理论，并通过Nozières–Luttinger构造推导出Landau泛函。对Bloch波扰动的瞬时响应在作用量中同时产生反常Berry联络势和相互作用诱导的准粒子电流的量子几何贡献。通过电磁Ward恒等式，守恒的物理电荷电流被获得为该量子几何电流与裸漂移电流的组合。因此，内禀反常霍尔电导率由修饰准粒子能带的Berry曲率积分决定，而Drude权重包含常规和量子几何两种贡献。在存在Galilei对称性的情况下，Drude权重受到保护免受相互作用重整化。在平坦/窄带极限下，输运主要由量子几何主导，并可被热增强。这些结果确立了准粒子占据数、Landau相互作用以及准粒子携带的量子几何作为Berry-Landau费米液体的基本低能要素。
英文摘要：
Landau Fermi-liquid theory characterizes interacting metals through quasiparticles and their residual interactions. It is a challenge to incorporate non-trivial quantum geometry -- as encoded by Berry phases and the quantum metric -- as a fundamental ingredient. We formulate a Berry-Landau Fermi-liquid theory for spinless fermions within an isolated band crossing the Fermi surface and derive the Landau functional through the Nozières--Luttinger construction. The instantaneous response to a perturbation of the Bloch waves generates both an anomalous Berry-connection potential in the action and an interaction-induced quantum-geometric contribution to the quasiparticle current. The conserved physical charge current is then obtained via the electromagnetic Ward identity as a combinati of this quantum-geometric current and the bare drift current. Therefore, the intrinsic anomalous Hall conductivity is fixed by the Berry-curvature integral of the dressed quasiparticle band while the Drude weight contains both conventional and quantum-geometric contributions. In the presence of Galilean symmetry, the Drude weight is protected against interaction renormalization. In the flat/narrow-band limit, transport is dominantly quantum-geometric and can be thermally enhanced. These results establish quasiparticle occupations, Landau interactions, and the quantum geometry carried by quasiparticles as the fundamental low-energy ingredients of a Berry-Landau Fermi liquid.
