Pinning of fermionic occupation numbers
<p style="text-align:justify;">The Pauli exclusion principle is a constraint on the natural occupation numbers of fermionic states. It has been suspected since at least the 1970s, and only proved very recently, that there is a multitude of further constraints on these numbers, gener...
| Main Authors: | , , |
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| Format: | Journal article |
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American Physical Society
2013
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| _version_ | 1826296356385325056 |
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| author | Schilling, C Gross, D Christandl, M |
| author_facet | Schilling, C Gross, D Christandl, M |
| author_sort | Schilling, C |
| collection | OXFORD |
| description | <p style="text-align:justify;">The Pauli exclusion principle is a constraint on the natural occupation numbers of fermionic states. It has been suspected since at least the 1970s, and only proved very recently, that there is a multitude of further constraints on these numbers, generalizing the Pauli principle. Here, we provide the first analytic analysis of the physical relevance of these constraints. We compute the natural occupation numbers for the ground states of a family of interacting fermions in a harmonic potential. Intriguingly, we find that the occupation numbers are almost, but not exactly, pinned to the boundary of the allowed region (quasipinned). The result suggests that the physics behind the phenomenon is richer than previously appreciated. In particular, it shows that for some models, the generalized Pauli constraints play a role for the ground state, even though they do not limit the ground-state energy. Our findings suggest a generalization of the Hartree-Fock approximation.</p> |
| first_indexed | 2024-03-07T04:15:04Z |
| format | Journal article |
| id | oxford-uuid:c9271b55-ee72-4f2b-a8f1-6d4d913d788a |
| institution | University of Oxford |
| last_indexed | 2024-03-07T04:15:04Z |
| publishDate | 2013 |
| publisher | American Physical Society |
| record_format | dspace |
| spelling | oxford-uuid:c9271b55-ee72-4f2b-a8f1-6d4d913d788a2022-03-27T06:57:01ZPinning of fermionic occupation numbersJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:c9271b55-ee72-4f2b-a8f1-6d4d913d788aSymplectic Elements at OxfordAmerican Physical Society2013Schilling, CGross, DChristandl, M <p style="text-align:justify;">The Pauli exclusion principle is a constraint on the natural occupation numbers of fermionic states. It has been suspected since at least the 1970s, and only proved very recently, that there is a multitude of further constraints on these numbers, generalizing the Pauli principle. Here, we provide the first analytic analysis of the physical relevance of these constraints. We compute the natural occupation numbers for the ground states of a family of interacting fermions in a harmonic potential. Intriguingly, we find that the occupation numbers are almost, but not exactly, pinned to the boundary of the allowed region (quasipinned). The result suggests that the physics behind the phenomenon is richer than previously appreciated. In particular, it shows that for some models, the generalized Pauli constraints play a role for the ground state, even though they do not limit the ground-state energy. Our findings suggest a generalization of the Hartree-Fock approximation.</p> |
| spellingShingle | Schilling, C Gross, D Christandl, M Pinning of fermionic occupation numbers |
| title | Pinning of fermionic occupation numbers |
| title_full | Pinning of fermionic occupation numbers |
| title_fullStr | Pinning of fermionic occupation numbers |
| title_full_unstemmed | Pinning of fermionic occupation numbers |
| title_short | Pinning of fermionic occupation numbers |
| title_sort | pinning of fermionic occupation numbers |
| work_keys_str_mv | AT schillingc pinningoffermionicoccupationnumbers AT grossd pinningoffermionicoccupationnumbers AT christandlm pinningoffermionicoccupationnumbers |