Unveiling Topological Fusion in Quantum Hall Systems from Microscopic Principles
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866910220617252864 |
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| author | Bochniak, Arkadiusz Ryu, Shinsei Fuchs, Jürgen Ortiz, Gerardo |
| author_facet | Bochniak, Arkadiusz Ryu, Shinsei Fuchs, Jürgen Ortiz, Gerardo |
| contents | Establishing the fusion rules of anyonic quasiparticles in fractional quantum Hall fluids is essential for understanding their underlying topological order. Building on the conjecture that key topological properties are encoded in the "DNA" of candidate many-body wave functions - that is, the pattern of dominant orbital occupations restricted to a finite number of lowest Landau levels - we propose a combinatorial framework that derives these fusion rules directly from microscopic data. By extending Schrieffer's counting argument and introducing classes of topological excitations, our framework provides a unified route to the fusion rules for both Abelian and non-Abelian excitations. This approach elucidates the emergence of topological features from first principles in both fermionic and bosonic systems. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2604_16525 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Unveiling Topological Fusion in Quantum Hall Systems from Microscopic Principles Bochniak, Arkadiusz Ryu, Shinsei Fuchs, Jürgen Ortiz, Gerardo Mesoscale and Nanoscale Physics Strongly Correlated Electrons Mathematical Physics Quantum Physics Establishing the fusion rules of anyonic quasiparticles in fractional quantum Hall fluids is essential for understanding their underlying topological order. Building on the conjecture that key topological properties are encoded in the "DNA" of candidate many-body wave functions - that is, the pattern of dominant orbital occupations restricted to a finite number of lowest Landau levels - we propose a combinatorial framework that derives these fusion rules directly from microscopic data. By extending Schrieffer's counting argument and introducing classes of topological excitations, our framework provides a unified route to the fusion rules for both Abelian and non-Abelian excitations. This approach elucidates the emergence of topological features from first principles in both fermionic and bosonic systems. |
| title | Unveiling Topological Fusion in Quantum Hall Systems from Microscopic Principles |
| topic | Mesoscale and Nanoscale Physics Strongly Correlated Electrons Mathematical Physics Quantum Physics |
| url | https://arxiv.org/abs/2604.16525 |