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| Format: | Preprint |
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2023
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| Online Access: | https://arxiv.org/abs/2306.14931 |
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| _version_ | 1866910411479056384 |
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| author | Mikhailov, S. A. |
| author_facet | Mikhailov, S. A. |
| contents | In a recent paper (arXiv:2206.05152v4), using the exact diagonalization technique, I calculated the energy and other physical properties (electron density, pair correlation function) of a system of $N\le 7$ two-dimensional electrons at the Landau level filling factor $ν=1/3$, and showed that the variational many-body wave function proposed for this filling factor by Laughlin is far from the true ground state. In this paper I continue to study exact properties of a small ($N\le 7$) system of two-dimensional electrons lying on the lowest Landau level. I analyze the energies and electron densities of the systems with $N\le 7$ electrons continuously as a function of the magnetic field in the range $1/4\lesssimν<1$. The physical mechanisms of the appearance of energy gaps in many-particle electron spectra are elucidated. The results obtained clarify the true nature of the ground and excited states of the considered systems. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2306_14931 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Toward a new theory of the fractional quantum Hall effect: The many-body spectra and energy gaps at $ν<1$ Mikhailov, S. A. Mesoscale and Nanoscale Physics Strongly Correlated Electrons Quantum Physics In a recent paper (arXiv:2206.05152v4), using the exact diagonalization technique, I calculated the energy and other physical properties (electron density, pair correlation function) of a system of $N\le 7$ two-dimensional electrons at the Landau level filling factor $ν=1/3$, and showed that the variational many-body wave function proposed for this filling factor by Laughlin is far from the true ground state. In this paper I continue to study exact properties of a small ($N\le 7$) system of two-dimensional electrons lying on the lowest Landau level. I analyze the energies and electron densities of the systems with $N\le 7$ electrons continuously as a function of the magnetic field in the range $1/4\lesssimν<1$. The physical mechanisms of the appearance of energy gaps in many-particle electron spectra are elucidated. The results obtained clarify the true nature of the ground and excited states of the considered systems. |
| title | Toward a new theory of the fractional quantum Hall effect: The many-body spectra and energy gaps at $ν<1$ |
| topic | Mesoscale and Nanoscale Physics Strongly Correlated Electrons Quantum Physics |
| url | https://arxiv.org/abs/2306.14931 |