Fractional quantum Hall effect in higher dimensions
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866929670890455040 |
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| author | Agarwal, Abhishek Karabali, Dimitra Nair, V. P. |
| author_facet | Agarwal, Abhishek Karabali, Dimitra Nair, V. P. |
| contents | Generalizing from previous work on the integer quantum Hall effect, we construct the effective action for the analog of Laughlin states for the fractional quantum Hall effect in higher dimensions. The formalism is a generalization of the parton picture used in two spatial dimensions, the crucial ingredient being the cancellation of anomalies for the gauge fields binding the partons together. Some subtleties which exist even in two dimensions are pointed out. The effective action is obtained from a combination of the Dolbeault and Dirac index theorems. We also present expressions for some transport coefficients such as Hall conductivity and Hall viscosity for the fractional states. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2410_14036 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Fractional quantum Hall effect in higher dimensions Agarwal, Abhishek Karabali, Dimitra Nair, V. P. High Energy Physics - Theory Strongly Correlated Electrons Mathematical Physics Generalizing from previous work on the integer quantum Hall effect, we construct the effective action for the analog of Laughlin states for the fractional quantum Hall effect in higher dimensions. The formalism is a generalization of the parton picture used in two spatial dimensions, the crucial ingredient being the cancellation of anomalies for the gauge fields binding the partons together. Some subtleties which exist even in two dimensions are pointed out. The effective action is obtained from a combination of the Dolbeault and Dirac index theorems. We also present expressions for some transport coefficients such as Hall conductivity and Hall viscosity for the fractional states. |
| title | Fractional quantum Hall effect in higher dimensions |
| topic | High Energy Physics - Theory Strongly Correlated Electrons Mathematical Physics |
| url | https://arxiv.org/abs/2410.14036 |