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arXiv · 2508.21502

Anyons in the $\pi$-flux phase of fermionic matter coupled to a $\mathbb{Z}_2$-gauge field

Sven Bachmann·Leonardo Goller·Marcello Porta
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Abstract

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 $\pi$-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 $\pi$-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.

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Sven Bachmann, Leonardo Goller, Marcello Porta. 2025-08-29. Anyons in the $\pi$-flux phase of fermionic matter coupled to a $\mathbb{Z}_2$-gauge field. https://arxiv.org/abs/2508.21502

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