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

Fuji, Yohei; Lecheminant, P.

doi:10.1103/PhysRevB.95.125130

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

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Fuji, Yohei
Max Planck Institute for the Physics of Complex Systems, Max Planck Society;

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https://journals.aps.org/prb/abstract/10.1103/PhysRevB.95.125130
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Citation

Fuji, Y., & Lecheminant, P. (2017). Non-Abelian SU (N-1)-singlet fractional quantum Hall states from coupled wires. Physical Review B, 95(12): 125130. doi:10.1103/PhysRevB.95.125130.

Cite as: https://hdl.handle.net/11858/00-001M-0000-002D-ADCF-6

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 v = k(N - 1)/[N + k(N - 1) m] labeled by integers k and m, which are potentially realized in multicomponent 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.