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Peer-reviewedCC BYComplex Analysis and Operator Theory

Exchange and Exclusion in the Non-abelian Anyon Gas

  • Douglas Lundholm1
  • Viktor Qvarfordt2
  1. 1Department of Mathematics, Uppsala University, Box 524, SE-751 20, Uppsala, Sweden
  2. 2Stockholm Mathematics Centre (SMC), Stockholm, Sweden
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Abstract

We review and develop the many-body spectral theory of ideal anyons, i.e. identical quantum particles in the plane whose exchange rules are governed by unitary representations of the braid group on N strands. Allowing for arbitrary rank (dependent on N ) and non-abelian representations, and letting N → ∞ N → ∞ , this defines the ideal non-abelian many-anyon gas. We compute exchange operators and phases for a common and wide class of representations defined by fusion algebras, including the Fibonacci and Ising anyon models. Furthermore, we extend methods of statistical repulsion (Poincaré and Hardy inequalities) and a local exclusion principle (also implying a Lieb–Thirring inequality) developed for abelian anyons to arbitrary geometric anyon models, i.e. arbitrary sequences of unitary representations of the braid group, for which two-anyon exchange is nontrivial.

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Cite

BibTeXRIS
BibTeX
@article{lundholm2026exchange,
  title = {{Exchange and Exclusion in the Non-abelian Anyon Gas}},
  author = {Douglas Lundholm and Viktor Qvarfordt},
  journal = {Complex Analysis and Operator Theory},
  year = {2026},
  month = oct,
  doi = {10.1007/s11785-026-02050-z},
  url = {https://doi.org/10.1007/s11785-026-02050-z},
  note = {CC BY},
}
RIS
TY  - JOUR
TI  - Exchange and Exclusion in the Non-abelian Anyon Gas
AU  - Douglas Lundholm
AU  - Viktor Qvarfordt
PY  - 2026
DA  - 2026/10/01
JO  - Complex Analysis and Operator Theory
DO  - 10.1007/s11785-026-02050-z
UR  - https://doi.org/10.1007/s11785-026-02050-z
AB  - We review and develop the many-body spectral theory of ideal anyons, i.e. identical quantum particles in the plane whose exchange rules are governed by unitary representations of the braid group on N strands. Allowing for arbitrary rank (dependent on N ) and non-abelian representations, and letting N → ∞ N → ∞ , this defines the ideal non-abelian many-anyon gas. We compute exchange operators and phases for a common and wide class of representations defined by fusion algebras, including the Fibonacci and Ising anyon models. Furthermore, we extend methods of statistical repulsion (Poincaré and Hardy inequalities) and a local exclusion principle (also implying a Lieb–Thirring inequality) developed for abelian anyons to arbitrary geometric anyon models, i.e. arbitrary sequences of unitary representations of the braid group, for which two-anyon exchange is nontrivial.
SN  - 1661-8254
SN  - 1661-8262
ER  -