Exchange and exclusion in the non-abelian anyon gas
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
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2020
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| author | Lundholm, Douglas Qvarfordt, Viktor |
| author_facet | Lundholm, Douglas Qvarfordt, Viktor |
| contents | 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 $N \to \infty$, 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2009_12709 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | Exchange and exclusion in the non-abelian anyon gas Lundholm, Douglas Qvarfordt, Viktor Mathematical Physics Quantum Gases Spectral Theory 81V27 (Primary) 81V70, 35P15, 20F36 (Secondary) 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 $N \to \infty$, 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. |
| title | Exchange and exclusion in the non-abelian anyon gas |
| topic | Mathematical Physics Quantum Gases Spectral Theory 81V27 (Primary) 81V70, 35P15, 20F36 (Secondary) |
| url | https://arxiv.org/abs/2009.12709 |