Corner Charge Fluctuations in Higher Dimensions
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arXiv
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| Main Authors: | , , , , , , |
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| Format: | Preprint |
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2026
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| _version_ | 1866909041055236096 |
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| author | Wu, Xiao-Chuan Tam, Pok Man Liang, Xuyang Liu, Zenan Yao, Dao-Xin Yan, Zheng Ryu, Shinsei |
| author_facet | Wu, Xiao-Chuan Tam, Pok Man Liang, Xuyang Liu, Zenan Yao, Dao-Xin Yan, Zheng Ryu, Shinsei |
| contents | Measuring charge fluctuations within a subregion provides a powerful probe of quantum many-body systems. In two spatial dimensions, the shape dependence of the dimensionless corner contribution encodes universal data of quantum critical points and reveals observables of quantum geometry in various quantum phases. Here, we systematically extend this framework to higher dimensions. In three dimensions, we derive the universal angle dependence associated with trihedral corners of a generic parallelepiped and benchmark the predictions against Monte Carlo simulations of lattice models at the O(3) quantum critical point. We further identify a wedge-corner contribution that directly probes the quantum metric, supported by numerical results for a lattice Weyl semimetal model. More generally, we obtain angle functions for polyhedral corners of arbitrary parallelotopes in general dimensions and clarify the scaling of the corner contribution across phases of matter. While insulators and conformal critical points exhibit similar behavior across dimensions, metals display a characteristic even-odd dimensional effect. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2605_13971 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Corner Charge Fluctuations in Higher Dimensions Wu, Xiao-Chuan Tam, Pok Man Liang, Xuyang Liu, Zenan Yao, Dao-Xin Yan, Zheng Ryu, Shinsei Strongly Correlated Electrons Mesoscale and Nanoscale Physics Statistical Mechanics High Energy Physics - Theory Measuring charge fluctuations within a subregion provides a powerful probe of quantum many-body systems. In two spatial dimensions, the shape dependence of the dimensionless corner contribution encodes universal data of quantum critical points and reveals observables of quantum geometry in various quantum phases. Here, we systematically extend this framework to higher dimensions. In three dimensions, we derive the universal angle dependence associated with trihedral corners of a generic parallelepiped and benchmark the predictions against Monte Carlo simulations of lattice models at the O(3) quantum critical point. We further identify a wedge-corner contribution that directly probes the quantum metric, supported by numerical results for a lattice Weyl semimetal model. More generally, we obtain angle functions for polyhedral corners of arbitrary parallelotopes in general dimensions and clarify the scaling of the corner contribution across phases of matter. While insulators and conformal critical points exhibit similar behavior across dimensions, metals display a characteristic even-odd dimensional effect. |
| title | Corner Charge Fluctuations in Higher Dimensions |
| topic | Strongly Correlated Electrons Mesoscale and Nanoscale Physics Statistical Mechanics High Energy Physics - Theory |
| url | https://arxiv.org/abs/2605.13971 |