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Quantum statistics transmutation via magnetic flux attachment

Gaultier Lambert, Douglas Lundholm and Nicolas Rougerie
Vol. 4 (2023), No. 4, 803–848
DOI: 10.2140/pmp.2023.4.803
Abstract

We consider a model for two types (bath and tracers) of 2D quantum particles in a perpendicular magnetic field. Interactions are short range and interspecies, and we assume that the bath particles are fermions, all lying in the lowest Landau level of the magnetic field. Heuristic arguments then indicate that, if the tracers are strongly coupled to the bath, they effectively change their quantum statistics, from bosonic to fermionic or vice-versa. We rigorously compute the energy of a natural trial state, indeed exhibiting this phenomenon of statistics transmutation. The proof involves estimates for the characteristic polynomial of the Ginibre ensemble of random matrices.

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Keywords
mathematical physics, many-body quantum mechanics, quantum hall effect, quantum statistics, anyons, Ginibre ensemble
Mathematical Subject Classification
Primary: 81V70
Milestones
Received: 8 February 2022
Revised: 26 January 2023
Accepted: 10 April 2023
Published: 29 November 2023
Authors
Gaultier Lambert
University of Zürich
Zürich
Switzerland
Douglas Lundholm
Department of Mathematics
Uppsala University
Uppsala
Sweden
Nicolas Rougerie
Unité de Mathématiques Pures et Appliquées
Ecole Normale Supérieure de Lyon & CNRS, UMPA (UMR 5669)
Lyon
France
© 2023 The Author(s), under exclusive license to MSP (Mathematical Sciences Publishers).