Phases of Interacting Fibonacci Anyons on a Ladder at Half-Filling

TL;DR

This paper explores the rich phase diagram of Fibonacci anyons on a two-leg ladder at half-filling, revealing metallic, insulating, and several ordered phases through numerical and perturbative methods.

Contribution

It introduces an effective one-dimensional model for Fibonacci anyons on a ladder and identifies four distinct phases using advanced numerical techniques.

Findings

Discovery of an anyonic metal at low interactions

Identification of a charge-density wave at strong repulsion

Characterization of four distinct phases including ferro- and antiferromagnetic chains

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, a $\mathbb{Z}_2$ phase, and an incommensurate phase.