Phase-shift instanton approach to tunneling duality in Read--Rezayi state
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arXiv
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| Autores principales: | , , , |
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| Formato: | Preprint |
| Publicado: |
2026
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| _version_ | 1866910184978251776 |
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| author | Ohashi, Ryoi Isobe, Hiroki Nakai, Ryota Nomura, Kentaro |
| author_facet | Ohashi, Ryoi Isobe, Hiroki Nakai, Ryota Nomura, Kentaro |
| contents | We study the duality between quasi-particle and electron tunneling in point-contact geometries of fractional quantum Hall states. To treat non-Abelian edge operators, we introduce a "phase-shift instanton" that incorporates phase factors from primary fields into the instanton gas framework. Using this method, we reformulate the Moore--Read duality and obtain an explicit dual description for the $k=3$ Read-Rezayi state. Our results clarify how quasi-particle tunneling produces characteristic phase shifts in instantons and how these shifts map strong quasi-particle tunneling to weak electron tunneling. Based on this dual description, we analytically evaluate the non-linear differential conductance in the strong-coupling regime. We reveal that, due to the physical requirement that the tunneling particle across the vacuum gap must be a true fermion, the transport behavior universally converges to a $G \propto V^4$ scaling for both the Moore--Read and Read--Rezayi states. This universal transport signature highlights a fundamental topological constraint underlying non-Abelian fractional quantum Hall edges. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_01206 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Phase-shift instanton approach to tunneling duality in Read--Rezayi state Ohashi, Ryoi Isobe, Hiroki Nakai, Ryota Nomura, Kentaro Mesoscale and Nanoscale Physics We study the duality between quasi-particle and electron tunneling in point-contact geometries of fractional quantum Hall states. To treat non-Abelian edge operators, we introduce a "phase-shift instanton" that incorporates phase factors from primary fields into the instanton gas framework. Using this method, we reformulate the Moore--Read duality and obtain an explicit dual description for the $k=3$ Read-Rezayi state. Our results clarify how quasi-particle tunneling produces characteristic phase shifts in instantons and how these shifts map strong quasi-particle tunneling to weak electron tunneling. Based on this dual description, we analytically evaluate the non-linear differential conductance in the strong-coupling regime. We reveal that, due to the physical requirement that the tunneling particle across the vacuum gap must be a true fermion, the transport behavior universally converges to a $G \propto V^4$ scaling for both the Moore--Read and Read--Rezayi states. This universal transport signature highlights a fundamental topological constraint underlying non-Abelian fractional quantum Hall edges. |
| title | Phase-shift instanton approach to tunneling duality in Read--Rezayi state |
| topic | Mesoscale and Nanoscale Physics |
| url | https://arxiv.org/abs/2605.01206 |