Incompressible quantum liquid on the four-dimensional sphere
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arXiv
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| Auteurs principaux: | , , , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866915787719049216 |
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| author | Zhao, Junwen Meng, Xue Zhu, Wei Wu, Congjun |
| author_facet | Zhao, Junwen Meng, Xue Zhu, Wei Wu, Congjun |
| contents | The study of quantum Hall effect (QHE) is a foundation of topological physics, inspiring extensive explorations of its high-dimensional generalizations. Notably, the four dimensional (4D) QHE has been experimentally realized in synthetic quantum systems, including cold atoms, photonic lattices, and metamaterials. However, the many-body effect in the 4D QHE system remains poorly understood. In this study, we explore this problem by formulating the microscopic wavefunctions inspired by Laughlin's seminal work. Employing a generalized pseudo-potential framework, we derive an exact microscopic Hamiltonian consisting of two-body projectors that annihilate the microscopic wavefunctions. Diagonalizations on a small size system show that the quasi-hole states remain zero energy while the quasi-particle states exhibit a finite gap, in consistency with an incompressible state. Furthermore, the pairing distribution is calculated to substantiate the liquid-like nature of the wavefunction. Our work provides a preliminary understanding to the fractional topological states in high dimension. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_17989 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Incompressible quantum liquid on the four-dimensional sphere Zhao, Junwen Meng, Xue Zhu, Wei Wu, Congjun Strongly Correlated Electrons Other Condensed Matter Quantum Gases High Energy Physics - Theory The study of quantum Hall effect (QHE) is a foundation of topological physics, inspiring extensive explorations of its high-dimensional generalizations. Notably, the four dimensional (4D) QHE has been experimentally realized in synthetic quantum systems, including cold atoms, photonic lattices, and metamaterials. However, the many-body effect in the 4D QHE system remains poorly understood. In this study, we explore this problem by formulating the microscopic wavefunctions inspired by Laughlin's seminal work. Employing a generalized pseudo-potential framework, we derive an exact microscopic Hamiltonian consisting of two-body projectors that annihilate the microscopic wavefunctions. Diagonalizations on a small size system show that the quasi-hole states remain zero energy while the quasi-particle states exhibit a finite gap, in consistency with an incompressible state. Furthermore, the pairing distribution is calculated to substantiate the liquid-like nature of the wavefunction. Our work provides a preliminary understanding to the fractional topological states in high dimension. |
| title | Incompressible quantum liquid on the four-dimensional sphere |
| topic | Strongly Correlated Electrons Other Condensed Matter Quantum Gases High Energy Physics - Theory |
| url | https://arxiv.org/abs/2508.17989 |