Assembling Fibonacci Anyons From a $\mathbb{Z}_3$ Parafermion Lattice Model

Understand

Recent concrete proposals suggest it is possible to engineer a two-dimensional bulk phase supporting non-Abelian Fibonacci anyons out of Abelian fractional quantum Hall systems.

• The low-energy degrees of freedom of such setups can be modeled as $\mathbb{Z}_3$ parafermions "hopping" on a two-dimensional lattice.
• We use the density matrix renormalization group to study a model of this type interpolating between the decoupled-chain, triangular-lattice, and square-lattice limits.
• The results show clear evidence of the Fibonacci phase over a wide region of the phase diagram, most notably including the isotropic triangular lattice point.