Nonrelativistic Conformal Invariance in Mesoscopic Two-Dimensional Fermi Gases
| Autor: | Bekassy, Viktor, Hofmann, Johannes |
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| Rok vydání: | 2021 |
| Předmět: | |
| Zdroj: | Phys. Rev. Lett. 128, 193401 (2022) |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1103/PhysRevLett.128.193401 |
| Popis: | Two-dimensional Fermi gases with universal short-range interactions are known to exhibit a quantum anomaly, where a classical scale and conformal invariance is broken by quantum effects at strong coupling. We argue that in a quasi two-dimensional geometry, a conformal window remains at weak interactions. Using degenerate perturbation theory, we verify the conformal symmetry by computing the energy spectrum of mesoscopic particle ensembles in a harmonic trap, which separates into conformal towers formed by so-called primary states and their center-of-mass and breathing-mode excitations, the latter having excitation energies at precisely twice the harmonic oscillator energy. In addition, using Metropolis importance sampling, we compute the hyperradial distribution function of the many-body wave functions, which are predicted by the conformal symmetry in closed analytical form. The weakly interacting Fermi gas constitutes a system where the nonrelativistic conformal symmetry can be revealed using elementary methods, and our results are testable in current experiments on mesoscopic Fermi gases. Comment: 7 pages, 4 figures + 9 pages of Supplemental Material |
| Databáze: | arXiv |
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