Rotating trapped fermions in two dimensions and the complex Ginibre ensemble: Exact results for the entanglement entropy and number variance
| Autor: | Bertrand Lacroix-A-Chez-Toine, Satya N. Majumdar, Grégory Schehr |
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| Přispěvatelé: | Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS), Université Paris-Sud - Paris 11 (UP11)-Centre National de la Recherche Scientifique (CNRS), Centre National de la Recherche Scientifique (CNRS)-Université Paris-Sud - Paris 11 (UP11) |
| Rok vydání: | 2019 |
| Předmět: |
Condensed Matter::Quantum Gases
Physics Observable Quantum entanglement Fermion 01 natural sciences [PHYS.PHYS.PHYS-GEN-PH]Physics [physics]/Physics [physics]/General Physics [physics.gen-ph] 010305 fluids & plasmas Matter waves and collective properties of cold atoms and molecules Quantum mechanics 0103 physical sciences 010306 general physics Fermi gas Ground state Scaling Random matrix Eigenvalues and eigenvectors |
| Zdroj: | Phys.Rev.A Phys.Rev.A, 2019, 99 (2), pp.021602. ⟨10.1103/PhysRevA.99.021602⟩ |
| ISSN: | 2469-9934 2469-9926 |
| Popis: | We establish an exact mapping between the positions of $N$ noninteracting fermions in a two-dimensional rotating harmonic trap in its ground state and the eigenvalues of the $N\ifmmode\times\else\texttimes\fi{}N$ complex Ginibre ensemble of random matrix theory (RMT). Using RMT techniques, we make precise predictions for the statistics of the positions of the fermions, both in the bulk as well as at the edge of the trapped Fermi gas. In addition, we compute exactly, for any finite $N$, the R\'enyi entanglement entropy and the number variance of a disk of radius $r$ in the ground state. We show that while these two quantities are proportional to each other in the (extended) bulk, this is no longer the case very close to the trap center nor at the edge. Near the edge, and for large $N$, we provide exact expressions for the scaling functions associated with these two observables. |
| Databáze: | OpenAIRE |
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