Magnetic Thomas-Fermi theory for 2D abelian anyons
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arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866915901992861696 |
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| author | Levitt, Antoine Lundholm, Douglas Rougerie, Nicolas |
| author_facet | Levitt, Antoine Lundholm, Douglas Rougerie, Nicolas |
| contents | Two-dimensional abelian anyons are, in the magnetic gauge picture, represented as fermions coupled to magnetic flux tubes. For the ground state of such a system in a trapping potential, we theoretically and numerically investigate a Hartree approximate model, obtained by restricting trial states to Slater determinants and introducing a self-consistent magnetic field, locally proportional to matter density. This leads to a fermionic variant of the Chern-Simons-Schr{ö}dinger system. We find that for dense systems, a semi-classical approximation yields qualitatively good results. Namely, we derive a density functional theory of magnetic Thomas-Fermi type, which correctly captures the trends of our numerical results. In particular, we explore the subtle dependence of the ground state with respect to the fraction of magnetic flux units attached to particles. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_13481 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Magnetic Thomas-Fermi theory for 2D abelian anyons Levitt, Antoine Lundholm, Douglas Rougerie, Nicolas Analysis of PDEs Mesoscale and Nanoscale Physics Quantum Gases Strongly Correlated Electrons Mathematical Physics Two-dimensional abelian anyons are, in the magnetic gauge picture, represented as fermions coupled to magnetic flux tubes. For the ground state of such a system in a trapping potential, we theoretically and numerically investigate a Hartree approximate model, obtained by restricting trial states to Slater determinants and introducing a self-consistent magnetic field, locally proportional to matter density. This leads to a fermionic variant of the Chern-Simons-Schr{ö}dinger system. We find that for dense systems, a semi-classical approximation yields qualitatively good results. Namely, we derive a density functional theory of magnetic Thomas-Fermi type, which correctly captures the trends of our numerical results. In particular, we explore the subtle dependence of the ground state with respect to the fraction of magnetic flux units attached to particles. |
| title | Magnetic Thomas-Fermi theory for 2D abelian anyons |
| topic | Analysis of PDEs Mesoscale and Nanoscale Physics Quantum Gases Strongly Correlated Electrons Mathematical Physics |
| url | https://arxiv.org/abs/2504.13481 |