Non-Abelian phases in two-component $\nu=2/3$ fractional quantum Hall states: Emergence of Fibonacci anyons

TL;DR

This paper numerically investigates the emergence of non-Abelian Fibonacci anyons in a bilayer fractional quantum Hall system at filling factor 2/3, revealing a topologically nontrivial phase with 6-fold degeneracy.

Contribution

It demonstrates the realization of a non-Abelian Fibonacci phase in a bilayer quantum Hall system through numerical solutions and topological characterization.

Findings

Identified a 6-fold ground-state degeneracy on the torus.

Measured topological entanglement entropy consistent with Fibonacci anyons.

Found the phase emerges under dominant interlayer hollow-core interactions.

Abstract

Recent theoretical insights into the possibility of non-Abelian phases in $\nu=2/3$ fractional quantum Hall states revived the interest in the numerical phase diagram of the problem. We investigate the effect of various kinds of two-body interlayer couplings on the $(330)$ bilayer state and exactly solve the Hamiltonian for up to $14$ electrons on sphere and torus geometries. We consider interlayer tunneling, short-ranged repulsive/attractive pseudopotential interactions and Coulomb repulsion. We find a 6-fold ground-state degeneracy on the torus when the interlayer hollow-core interaction is dominant. To identify the topological nature of this phase we measure the orbital-cut entanglement spectrum, quasihole counting, topological entanglement entropy, and wave-function overlap. Comparing the numerical results to the theoretical predictions, we interpret this 6-fold ground-state degeneracy phase to be the non-Abelian bilayer Fibonacci state.