Non-Abelian SU(N-1)-singlet fractional quantum Hall states from coupled wires

TL;DR

This paper extends the coupled-wire construction method to realize non-Abelian SU(N-1)-singlet fractional quantum Hall states, analyzing their quasiparticles, edge states, and potential lattice system applications.

Contribution

It introduces a novel construction of non-Abelian SU(N-1)-singlet FQH states using coupled wires, with detailed CFT descriptions and potential realizations in lattice models.

Findings

Bulk quasiparticles described by Gepner parafermion CFT

Edge excitations characterized by multi-component free-boson CFT

Proposed applications to multi-component quantum Hall and spin systems

Abstract

The construction of fractional quantum Hall (FQH) states from the two-dimensional array of quantum wires provides a useful way to control strong interactions in microscopic models and has been successfully applied to the Laughlin, Moore-Read, and Read-Rezayi states. We extend this construction to the Abelian and non-Abelian $SU(N-1)$-singlet FQH states at filling fraction $\nu=k(N-1)/[N+k(N-1)m]$ labeled by integers $k$ and $m$, which are potentially realized in multi-component quantum Hall systems or $SU(N)$ spin systems. Utilizing the bosonization approach and conformal field theory (CFT), we show that their bulk quasiparticles and gapless edge excitations are both described by an $(N-1)$-component free-boson CFT and the $SU(N)_k/[U(1)]^{N-1}$ CFT known as the Gepner parafermion. Their generalization to different filling fractions is also proposed. In addition, we argue possible applications of these results to two kinds of lattice systems: bosons interacting via occupation-dependent correlated hoppings and an $SU(N)$ Heisenberg model.