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| Main Authors: | , |
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| Format: | Preprint |
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2024
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| Online Access: | https://arxiv.org/abs/2410.00958 |
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| _version_ | 1866909332584529920 |
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| author | Kaviraj, Apratim van Vliet, Philine |
| author_facet | Kaviraj, Apratim van Vliet, Philine |
| contents | We explore a supersymmetric (SUSY) theory that arises in the Landau level problem with disorder. Charged particles in a strong magnetic field and a local potential are described by small excitations around the ground state, the lowest Landau level (LLL). Around forty years ago Brézin, Gross and Itzykson showed that for a disorder potential certain observables in the LLL limit are described by a chiral SUSY theory. As a consequence, the problem undergoes a dimensional reduction by two dimensions, simplifying the computations. We generalize their findings by identifying the chiral SUSY as a special limit of a `magnetic Parisi-Sourlas (PS)' theory. The latter is a modification of the theories associated to fixed points of random field models. We show that the SUSY features extend to a much larger class of observables and to higher Landau levels. Finally we identify a set of new super-Ward identities and show how observables in the disordered theory must satisfy them. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_00958 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Supersymmetry in the Landau Level Problem with a Disorder Potential Kaviraj, Apratim van Vliet, Philine Mesoscale and Nanoscale Physics Disordered Systems and Neural Networks Statistical Mechanics High Energy Physics - Theory We explore a supersymmetric (SUSY) theory that arises in the Landau level problem with disorder. Charged particles in a strong magnetic field and a local potential are described by small excitations around the ground state, the lowest Landau level (LLL). Around forty years ago Brézin, Gross and Itzykson showed that for a disorder potential certain observables in the LLL limit are described by a chiral SUSY theory. As a consequence, the problem undergoes a dimensional reduction by two dimensions, simplifying the computations. We generalize their findings by identifying the chiral SUSY as a special limit of a `magnetic Parisi-Sourlas (PS)' theory. The latter is a modification of the theories associated to fixed points of random field models. We show that the SUSY features extend to a much larger class of observables and to higher Landau levels. Finally we identify a set of new super-Ward identities and show how observables in the disordered theory must satisfy them. |
| title | Supersymmetry in the Landau Level Problem with a Disorder Potential |
| topic | Mesoscale and Nanoscale Physics Disordered Systems and Neural Networks Statistical Mechanics High Energy Physics - Theory |
| url | https://arxiv.org/abs/2410.00958 |