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| Format: | Preprint |
| Published: |
2026
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| Online Access: | https://arxiv.org/abs/2605.25053 |
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| _version_ | 1866917529180438528 |
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| author | Wu, Xiaoguang |
| author_facet | Wu, Xiaoguang |
| contents | A GW-BSE approximation scheme is assessed by applying it to a model of asymmetric two-dimensional (2D) interacting electron system. The model is assumed to have a parabolic band characterized by two independent effective mass parameters. A perpendicular magnetic field is applied to the asymmetric 2D electron system, and the well-known Kohn's theorem is still valid, i.e., the cyclotron resonance is not affected by the electron-electron interaction. This theorem imposes a constraint on the approximation scheme employed in the treatment of electron-electron interaction. In the present study, the Green's function is calculated in the self-consistent Hartree-Fock approximation. The electron density correlation function is calculated by solving a Bethe-Salpeter equation (BSE) in the ladder diagram approximation. It is found that, the excitation frequency near the cyclotron resonance frequency approaches a value that is lower than the cyclotron resonance frequency at small wave vectors, when two effective masses are different. When two effective masses are the same, the excitation frequency approaches the cyclotron resonance frequency at small wave vectors as required. Our findings suggest that the approximation scheme used in this theoretical investigation fails to satisfy the requirement due to the Kohn's theorem, and one should go beyond this approximation scheme. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_25053 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Assessment of a GW-BSE approximation scheme on an asymmetric two-dimensional interacting electron system in a perpendicular magnetic field Wu, Xiaoguang Materials Science A GW-BSE approximation scheme is assessed by applying it to a model of asymmetric two-dimensional (2D) interacting electron system. The model is assumed to have a parabolic band characterized by two independent effective mass parameters. A perpendicular magnetic field is applied to the asymmetric 2D electron system, and the well-known Kohn's theorem is still valid, i.e., the cyclotron resonance is not affected by the electron-electron interaction. This theorem imposes a constraint on the approximation scheme employed in the treatment of electron-electron interaction. In the present study, the Green's function is calculated in the self-consistent Hartree-Fock approximation. The electron density correlation function is calculated by solving a Bethe-Salpeter equation (BSE) in the ladder diagram approximation. It is found that, the excitation frequency near the cyclotron resonance frequency approaches a value that is lower than the cyclotron resonance frequency at small wave vectors, when two effective masses are different. When two effective masses are the same, the excitation frequency approaches the cyclotron resonance frequency at small wave vectors as required. Our findings suggest that the approximation scheme used in this theoretical investigation fails to satisfy the requirement due to the Kohn's theorem, and one should go beyond this approximation scheme. |
| title | Assessment of a GW-BSE approximation scheme on an asymmetric two-dimensional interacting electron system in a perpendicular magnetic field |
| topic | Materials Science |
| url | https://arxiv.org/abs/2605.25053 |