A Calogero model for the non-Abelian quantum Hall effect
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866916105305456640 |
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| author | Bourgine, Jean-Emile Matsuo, Yutaka |
| author_facet | Bourgine, Jean-Emile Matsuo, Yutaka |
| contents | A model of the non-Abelian fractional quantum Hall effect is obtained from the diagonalization of the matrix model proposed by Dorey, Tong, and Turner (DTT). The Hamiltonian is reminiscent of a spin Calogero-Moser model but involves higher-order symmetric representations of the non-Abelian symmetry. We derive the energy spectrum and show that the Hamiltonian has a triangular action on a certain class of wave functions with a free fermion expression. We deduce the expression of the ground states eigenfunctions and show that they solve a Knizhnik-Zamolodchikov equation. Finally, we discuss the emergence of Kac-Moody symmetries in the large $N$ limit using the level-rank duality and confirm the results obtained previously by DTT. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_03087 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A Calogero model for the non-Abelian quantum Hall effect Bourgine, Jean-Emile Matsuo, Yutaka High Energy Physics - Theory Strongly Correlated Electrons Mathematical Physics A model of the non-Abelian fractional quantum Hall effect is obtained from the diagonalization of the matrix model proposed by Dorey, Tong, and Turner (DTT). The Hamiltonian is reminiscent of a spin Calogero-Moser model but involves higher-order symmetric representations of the non-Abelian symmetry. We derive the energy spectrum and show that the Hamiltonian has a triangular action on a certain class of wave functions with a free fermion expression. We deduce the expression of the ground states eigenfunctions and show that they solve a Knizhnik-Zamolodchikov equation. Finally, we discuss the emergence of Kac-Moody symmetries in the large $N$ limit using the level-rank duality and confirm the results obtained previously by DTT. |
| title | A Calogero model for the non-Abelian quantum Hall effect |
| topic | High Energy Physics - Theory Strongly Correlated Electrons Mathematical Physics |
| url | https://arxiv.org/abs/2401.03087 |