Anyons in the $π$-flux phase of fermionic matter coupled to a $\mathbb{Z}_2$-gauge field
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866917086156029952 |
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| author | Bachmann, Sven Goller, Leonardo Porta, Marcello |
| author_facet | Bachmann, Sven Goller, Leonardo Porta, Marcello |
| contents | We consider a system of weakly interacting spinful lattice fermions coupled to a dynamical $\mathbb{Z}_2$ gauge field. Using reflection positivity, we prove that the ground state lies in the sector of a uniform $π$-flux per plaquette and that the monopoles are massive. In the presence of a staggered mass for the fermions, this yields a fully gapped, four-dimensional ground state space on large tori. It is topologically ordered. By considering adiabatic $π$-flux insertion, we construct dressed monopole excitations, show that their self-braiding is proportional to the Hall conductance and hence vanishes, and prove that their braiding with the fermionic excitations is that of the toric code. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_21502 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Anyons in the $π$-flux phase of fermionic matter coupled to a $\mathbb{Z}_2$-gauge field Bachmann, Sven Goller, Leonardo Porta, Marcello Mathematical Physics Strongly Correlated Electrons We consider a system of weakly interacting spinful lattice fermions coupled to a dynamical $\mathbb{Z}_2$ gauge field. Using reflection positivity, we prove that the ground state lies in the sector of a uniform $π$-flux per plaquette and that the monopoles are massive. In the presence of a staggered mass for the fermions, this yields a fully gapped, four-dimensional ground state space on large tori. It is topologically ordered. By considering adiabatic $π$-flux insertion, we construct dressed monopole excitations, show that their self-braiding is proportional to the Hall conductance and hence vanishes, and prove that their braiding with the fermionic excitations is that of the toric code. |
| title | Anyons in the $π$-flux phase of fermionic matter coupled to a $\mathbb{Z}_2$-gauge field |
| topic | Mathematical Physics Strongly Correlated Electrons |
| url | https://arxiv.org/abs/2508.21502 |