Curvature-Flux Representation of Local Dirac-Node Topology from Non-Hermitian Zeeman Quantum Geometry

Abstract:Local Dirac-node topology is usually described by a winding number or Berry phase, whereas curvature-flux formulations are commonly associated with global band topology. Here we show that the non-Hermitian Zeeman quantum geometric tensor (QGT) provides a curvature-flux representation of local $\pi_1$ topology. Unlike the conventional Hermitian QGT, whose metric and Berry curvature are fixed respectively by its real symmetric and imaginary antisymmetric parts, the Zeeman QGT must be decomposed according to symmetry under index exchange. This decomposition yields normal and anomalous metric-curvature sectors. The normal sector has the same metric-curvature structure as the conventional Hermitian QGT. The anomalous sector, by contrast, contains two components absent in the conventional QGT: an imaginary symmetric metric-like tensor and a real antisymmetric curvature-like tensor. In a two-dimensional Dirac system, the anomalous Zeeman curvature forms a radial flux field Hodge-dual to the tangential winding field of the Dirac node, thereby converting the local winding invariant into a Gauss-type flux invariant. We further show that the four Zeeman-geometric sectors map one-to-one onto frequency- and symmetry-resolved gyrotropic conductivity channels, with reciprocal kinetic magnetoelectric response providing a complementary probe. These results establish non-Hermitian Zeeman quantum geometry as a measurable framework connecting local Dirac-node topology and transport.

Quantum Physics (quant-ph); Mesoscale and Nanoscale Physics (cond-mat.mes-hall); Materials Science (cond-mat.mtrl-sci)

arXiv:2604.09725 [quant-ph]

(or arXiv:2604.09725v3 [quant-ph] for this version)

https://doi.org/10.48550/arXiv.2604.09725 Focus to learn more arXiv-issued DOI via DataCite

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