--- res: bibo_abstract: - 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 Haldaneā€™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.@eng bibo_authorlist: - foaf_Person: foaf_givenName: Robert foaf_name: Seiringer, Robert foaf_surname: Seiringer foaf_workInfoHomepage: http://www.librecat.org/personId=4AFD0470-F248-11E8-B48F-1D18A9856A87 orcid: 0000-0002-6781-0521 - foaf_Person: foaf_givenName: Jakob foaf_name: Yngvason, Jakob foaf_surname: Yngvason bibo_doi: 10.1007/s10955-020-02586-0 bibo_volume: 181 dct_date: 2020^xs_gYear dct_identifier: - UT:000543030000002 dct_isPartOf: - http://id.crossref.org/issn/00224715 - http://id.crossref.org/issn/15729613 dct_language: eng dct_publisher: Springer@ dct_title: Emergence of Haldane pseudo-potentials in systems with short-range interactions@ ...