--- _id: '8091' abstract: - lang: eng text: In the setting of the fractional quantum Hall effect we study the effects of strong, repulsive two-body interaction potentials of short range. We prove that Haldane’s pseudo-potential operators, including their pre-factors, emerge as mathematically rigorous limits of such interactions when the range of the potential tends to zero while its strength tends to infinity. In a common approach the interaction potential is expanded in angular momentum eigenstates in the lowest Landau level, which amounts to taking the pre-factors to be the moments of the potential. Such a procedure is not appropriate for very strong interactions, however, in particular not in the case of hard spheres. We derive the formulas valid in the short-range case, which involve the scattering lengths of the interaction potential in different angular momentum channels rather than its moments. Our results hold for bosons and fermions alike and generalize previous results in [6], which apply to bosons in the lowest angular momentum channel. Our main theorem asserts the convergence in a norm-resolvent sense of the Hamiltonian on the whole Hilbert space, after appropriate energy scalings, to Hamiltonians with contact interactions in the lowest Landau level. acknowledgement: "Open access funding provided by Institute of Science and Technology (IST Austria).\r\nThe work of R.S. was supported by the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (Grant Agreement No 694227). J.Y. gratefully acknowledges hospitality at the LPMMC Grenoble and valuable discussions with Alessandro Olgiati and Nicolas Rougerie. " article_processing_charge: Yes (via OA deal) article_type: original author: - first_name: Robert full_name: Seiringer, Robert id: 4AFD0470-F248-11E8-B48F-1D18A9856A87 last_name: Seiringer orcid: 0000-0002-6781-0521 - first_name: Jakob full_name: Yngvason, Jakob last_name: Yngvason citation: ama: Seiringer R, Yngvason J. Emergence of Haldane pseudo-potentials in systems with short-range interactions. Journal of Statistical Physics. 2020;181:448-464. doi:10.1007/s10955-020-02586-0 apa: Seiringer, R., & Yngvason, J. (2020). Emergence of Haldane pseudo-potentials in systems with short-range interactions. Journal of Statistical Physics. Springer. https://doi.org/10.1007/s10955-020-02586-0 chicago: Seiringer, Robert, and Jakob Yngvason. “Emergence of Haldane Pseudo-Potentials in Systems with Short-Range Interactions.” Journal of Statistical Physics. Springer, 2020. https://doi.org/10.1007/s10955-020-02586-0. ieee: R. Seiringer and J. Yngvason, “Emergence of Haldane pseudo-potentials in systems with short-range interactions,” Journal of Statistical Physics, vol. 181. Springer, pp. 448–464, 2020. ista: Seiringer R, Yngvason J. 2020. Emergence of Haldane pseudo-potentials in systems with short-range interactions. Journal of Statistical Physics. 181, 448–464. mla: Seiringer, Robert, and Jakob Yngvason. “Emergence of Haldane Pseudo-Potentials in Systems with Short-Range Interactions.” Journal of Statistical Physics, vol. 181, Springer, 2020, pp. 448–64, doi:10.1007/s10955-020-02586-0. short: R. Seiringer, J. Yngvason, Journal of Statistical Physics 181 (2020) 448–464. date_created: 2020-07-05T22:00:46Z date_published: 2020-10-01T00:00:00Z date_updated: 2023-08-22T07:51:47Z day: '01' ddc: - '530' department: - _id: RoSe doi: 10.1007/s10955-020-02586-0 ec_funded: 1 external_id: arxiv: - '2001.07144' isi: - '000543030000002' file: - access_level: open_access checksum: 5cbeef52caf18d0d952f17fed7b5545a content_type: application/pdf creator: dernst date_created: 2020-11-25T15:05:04Z date_updated: 2020-11-25T15:05:04Z file_id: '8812' file_name: 2020_JourStatPhysics_Seiringer.pdf file_size: 404778 relation: main_file success: 1 file_date_updated: 2020-11-25T15:05:04Z has_accepted_license: '1' intvolume: ' 181' isi: 1 language: - iso: eng month: '10' oa: 1 oa_version: Published Version page: 448-464 project: - _id: B67AFEDC-15C9-11EA-A837-991A96BB2854 name: IST Austria Open Access Fund - _id: 25C6DC12-B435-11E9-9278-68D0E5697425 call_identifier: H2020 grant_number: '694227' name: Analysis of quantum many-body systems publication: Journal of Statistical Physics publication_identifier: eissn: - '15729613' issn: - '00224715' publication_status: published publisher: Springer quality_controlled: '1' scopus_import: '1' status: public title: Emergence of Haldane pseudo-potentials in systems with short-range interactions tmp: image: /images/cc_by.png legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0) short: CC BY (4.0) type: journal_article user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8 volume: 181 year: '2020' ...