Fractional quantum Hall effect in a U(1)xSU(2) gauge field

Abstract

We consider the bosonic fractional quantum Hall effect in the presence of a non-Abelian gauge field in addition to the usual Abelian magnetic field. The non-Abelian field breaks the twofold internal state degeneracy, but preserves the Landau level degeneracy. Using exact diagonalization, we find that for moderate non-Abelian field strengths the system's behaviour resembles a single internal state quantum Hall system, while for stronger fields there is a phase transition to either two internal state behaviour or the complete absence of fractional quantum Hall plateaus. Usually the energy gap is reduced by the presence of a non-Abelian field, but some non-Abelian fields appear to slightly increase the gap of the $\nu =1$ and $\nu =3/2$ Read-Rezayi states.

15 pages, 8 figures, submitted to New J. Phys

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Cited by in corpus (13)

• Light-induced gauge fields for ultracold atoms
• Unconventional states of bosons with synthetic spin-orbit coupling
• Non-Abelian spin singlet states of two-component Bose gases in artificial gauge fields
• Ultracold atoms in U(2) non-Abelian gauge potentials preserving the Landau levels
• Focus on topological quantum computation
• Topological phase transitions driven by non-Abelian gauge potentials in optical square lattices
• Fractional quantum Hall states of a Bose gas with spin-orbit coupling
• Vortex lattices for ultracold bosonic atoms in a non-Abelian gauge potential
• Fragility of the fractional quantum spin Hall effect in quantum gases
• The Geometry of (non-Abelian) Landau levels
• Strongly correlated states of trapped ultracold fermions in deformed Landau levels
• The N = 1 Supersymmetric Wong Equations and the Non-Abelian Landau Problem
• Topological quantum electrodynamics in synthetic non-Abelian gauge fields