Dual Quantum Geometric Tensors and Local Topological Invariant
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| Format: | Preprint |
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2026
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| author | Cui, Rongjie Xiang, Longjun Xu, Fuming Wang, Jian |
| author_facet | Cui, Rongjie Xiang, Longjun Xu, Fuming Wang, Jian |
| contents | The conventional quantum geometric tensor (QGT) is Hermitian, with a real symmetric quantum metric and an imaginary antisymmetric Berry curvature. We show that the Zeeman QGT is generically non-Hermitian and admits a natural decomposition into normal and anomalous metric-curvature sectors. The normal sector reduces to the conventional Hermitian structure, whereas the anomalous sector contains an imaginary symmetric metric-like tensor and a real antisymmetric curvature-like tensor with no counterpart in the standard QGT. In a two-dimensional Dirac system, the anomalous Zeeman curvature develops a radial flux singularity that is Hodge-dual to the tangential winding field of the Dirac node. This recasts the same local $π_1$ topology into a curvature-flux language, analogous to the flux representation of global $π_2$ topology by the conventional Berry curvature. At the level of linear response, the four symmetry-resolved components of the gyrotropic conductivity are in one-to-one correspondence with the four components of the Zeeman QGT, while their distinct low-frequency scalings provide an additional diagnostic for isolating the underlying geometric sector. The reciprocal kinetic magnetoelectric response offers a complementary experimental route to probe the same structure. These results establish a unified framework connecting non-Hermitian Zeeman quantum geometry, local Dirac-node topology, and measurable transport signatures. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2604_09725 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Dual Quantum Geometric Tensors and Local Topological Invariant Cui, Rongjie Xiang, Longjun Xu, Fuming Wang, Jian Quantum Physics Mesoscale and Nanoscale Physics Materials Science The conventional quantum geometric tensor (QGT) is Hermitian, with a real symmetric quantum metric and an imaginary antisymmetric Berry curvature. We show that the Zeeman QGT is generically non-Hermitian and admits a natural decomposition into normal and anomalous metric-curvature sectors. The normal sector reduces to the conventional Hermitian structure, whereas the anomalous sector contains an imaginary symmetric metric-like tensor and a real antisymmetric curvature-like tensor with no counterpart in the standard QGT. In a two-dimensional Dirac system, the anomalous Zeeman curvature develops a radial flux singularity that is Hodge-dual to the tangential winding field of the Dirac node. This recasts the same local $π_1$ topology into a curvature-flux language, analogous to the flux representation of global $π_2$ topology by the conventional Berry curvature. At the level of linear response, the four symmetry-resolved components of the gyrotropic conductivity are in one-to-one correspondence with the four components of the Zeeman QGT, while their distinct low-frequency scalings provide an additional diagnostic for isolating the underlying geometric sector. The reciprocal kinetic magnetoelectric response offers a complementary experimental route to probe the same structure. These results establish a unified framework connecting non-Hermitian Zeeman quantum geometry, local Dirac-node topology, and measurable transport signatures. |
| title | Dual Quantum Geometric Tensors and Local Topological Invariant |
| topic | Quantum Physics Mesoscale and Nanoscale Physics Materials Science |
| url | https://arxiv.org/abs/2604.09725 |