Non-Abelian Quantum Hall Effect in Topological Flat Bands

TL;DR

This paper provides numerical evidence for a non-Abelian quantum Hall effect in lattice models with topological flat bands, demonstrating stable ground states, quantized Chern numbers, and Moore-Read-like quasihole spectra.

Contribution

It is the first to numerically demonstrate a stable bosonic non-Abelian quantum Hall phase in a lattice topological flat band model.

Findings

Evidence of a stable $ u=1$ bosonic NA-QHE with three-fold ground state degeneracy.

Quantized Chern number confirming topological order.

Finite energy gap in quasihole spectrum with Moore-Read state counting.

Abstract

Inspired by recent theoretical discovery of robust fractional topological phases without a magnetic field, we search for the non-Abelian quantum Hall effect (NA-QHE) in lattice models with topological flat bands (TFBs). Through extensive numerical studies on the Haldane model with three-body hard-core bosons loaded into a TFB, we find convincing numerical evidence of a stable $\nu=1$ bosonic NA-QHE, with the characteristic three-fold quasi-degeneracy of ground states on a torus, a quantized Chern number, and a robust spectrum gap. Moreover, the spectrum for two-quasihole states also shows a finite energy gap, with the number of states in the lower energy sector satisfying the same counting rule as the Moore-Read Pfaffian state.