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Phases of interacting Fibonacci anyons on a ladder at half-filling

Nico Kirchner1,2, Roderich Moessner3, Frank Pollmann1,2, and Adam Gammon-Smith4,5

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Phys. Rev. B 114, 045117 – Published 17 July, 2026

DOI: https://doi.org/10.1103/c92g-mhly

Abstract

Two-dimensional many-body quantum systems can exhibit topological order and support collective excitations with anyonic statistics different from the usual fermionic or bosonic ones. With the emergence of these exotic point-like particles, it is natural to ask what phases can arise in interacting many-anyon systems. To study this topic, we consider the particular case of Fibonacci anyons subject to an anyonic tight-binding model with nearest-neighbor repulsion on a two-leg ladder. Focusing on the case of half-filling, for low interaction strengths an “anyonic” metal is found, whereas for strong repulsion, the anyons form an insulating charge-density wave. Within the latter regime, we introduce an effective one-dimensional model up to sixth order in perturbation theory arising from anyonic superexchange processes. We numerically identify four distinct phases of the effective model, which we characterize using matrix product state methods. These include both the ferro- and antiferromagnetic golden chain phases, as well as phases with Z2 and incommensurate correlations.

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Phys. Rev. B 114, 045117– Published 17 July, 2026
  • Received 28 October 2025
  • Revised 8 March 2026
  • Accepted 23 June 2026
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

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