Collective states of interacting Fibonacci anyons

TL;DR

This paper explores the diverse collective ground states of interacting Fibonacci anyons, revealing a rich phase diagram with critical and gapped phases, characterized by conformal field theories and topological symmetries.

Contribution

It generalizes the Majumdar-Ghosh Hamiltonian to anyonic systems, introducing three-anyon exchanges and analyzing their impact on phase structure.

Findings

Identification of multiple critical and gapped phases

Numerical confirmation of conformal field theory descriptions

Topological symmetry protection of critical phases

Abstract

We show that chains of interacting Fibonacci anyons can support a wide variety of collective ground states ranging from extended critical, gapless phases to gapped phases with ground-state degeneracy and quasiparticle excitations. In particular, we generalize the Majumdar-Ghosh Hamiltonian to anyonic degrees of freedom by extending recently studied pairwise anyonic interactions to three-anyon exchanges. The energetic competition between two- and three-anyon interactions leads to a rich phase diagram that harbors multiple critical and gapped phases. For the critical phases and their higher symmetry endpoints we numerically establish descriptions in terms of two-dimensional conformal field theories. A topological symmetry protects the critical phases and determines the nature of gapped phases.