Fidelity and quantum geometry approach to Dirac exceptional points in diamond nitrogen-vacancy centers
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866914447308619776 |
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| author | Ju, Chia-Yi Möller, Gunnar Tzeng, Yu-Chin |
| author_facet | Ju, Chia-Yi Möller, Gunnar Tzeng, Yu-Chin |
| contents | Dirac exceptional points (EPs) represent a novel class of non-Hermitian singularities that, unlike conventional EPs, reside entirely within the parity-time unbroken phase and exhibit linear energy dispersion. Here, we theoretically investigate the quantum geometry of Dirac EPs realized in nitrogen-vacancy centers in diamond, utilizing fidelity susceptibility as a probe. We demonstrate that despite the absence of a symmetry-breaking phase transition, the Dirac EP induces a pronounced geometric singularity, confirming the validity of the fidelity in characterizing non-Hermitian EPs. Specifically, the real part of the fidelity susceptibility diverges to negative infinity, which serves as a signature of non-Hermitian criticality. Crucially, however, we reveal that this divergence exhibits a distinct anisotropy, diverging along the non-reciprocal coupling direction while remaining finite along the detuning axis. Furthermore, we establish that this anisotropy, characterized by at least one exact dark direction coexisting with divergent directions, is a generic consequence of the Dirac EP structure whenever the parameter derivatives collectively span the off-diagonal operator space at the Dirac EP. This behavior stands in stark contrast to the omnidirectional divergence observed in conventional EPs. Our findings provide a comprehensive picture of the fidelity probe near the Dirac EP, highlighting the critical role of parameter directionality in exploiting Dirac EPs for quantum control and sensing applications. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_00666 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Fidelity and quantum geometry approach to Dirac exceptional points in diamond nitrogen-vacancy centers Ju, Chia-Yi Möller, Gunnar Tzeng, Yu-Chin Quantum Physics Mesoscale and Nanoscale Physics High Energy Physics - Theory Applied Physics Atomic and Molecular Clusters Dirac exceptional points (EPs) represent a novel class of non-Hermitian singularities that, unlike conventional EPs, reside entirely within the parity-time unbroken phase and exhibit linear energy dispersion. Here, we theoretically investigate the quantum geometry of Dirac EPs realized in nitrogen-vacancy centers in diamond, utilizing fidelity susceptibility as a probe. We demonstrate that despite the absence of a symmetry-breaking phase transition, the Dirac EP induces a pronounced geometric singularity, confirming the validity of the fidelity in characterizing non-Hermitian EPs. Specifically, the real part of the fidelity susceptibility diverges to negative infinity, which serves as a signature of non-Hermitian criticality. Crucially, however, we reveal that this divergence exhibits a distinct anisotropy, diverging along the non-reciprocal coupling direction while remaining finite along the detuning axis. Furthermore, we establish that this anisotropy, characterized by at least one exact dark direction coexisting with divergent directions, is a generic consequence of the Dirac EP structure whenever the parameter derivatives collectively span the off-diagonal operator space at the Dirac EP. This behavior stands in stark contrast to the omnidirectional divergence observed in conventional EPs. Our findings provide a comprehensive picture of the fidelity probe near the Dirac EP, highlighting the critical role of parameter directionality in exploiting Dirac EPs for quantum control and sensing applications. |
| title | Fidelity and quantum geometry approach to Dirac exceptional points in diamond nitrogen-vacancy centers |
| topic | Quantum Physics Mesoscale and Nanoscale Physics High Energy Physics - Theory Applied Physics Atomic and Molecular Clusters |
| url | https://arxiv.org/abs/2602.00666 |