Unconventional Filling Factor 4/11: A Closed-Form Ground State Wave Function

Abstract

The ground state at 4/11 filling factor is very well understood [Phys. Rev. Lett. 112, 016801 (2014)] in terms of the 1/3 filled second effective Landau level of the composite fermions whose correlations resemble with that of electrons in the ground state of two-body Haldane pseudo-potential of relative angular momentum 3, $V_3$. We here propose a closed-form ground state wave function for $V_3$ at 1/3 filling factor. We successfully compare it with the exact wave function for the systems with a few electrons, by calculating their mutual overlap, pair-correlation function, and entanglement spectra. By numerical exact diagonalization for a few electron systems, we find a window of nonzero $V_3$ is essential together with $V_1$ for being 4/11 state incompressible. The constructed wave function for 4/11 state using this proposed wave function has satisfactorily high overlap with the previously studied composite-fermion-diagonalized ground state wave function.

arXiv comment10 pages, 5 figures

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Cited by in corpus (7)

• Abelian parton state for the $\nu =4/11$ fractional quantum Hall effect
• Nature of the anomalous $4/13$ fractional quantum Hall effect in graphene
• An Anomalous Reentrant 5/2 Quantum Hall Phase at Moderate Landau-Level-Mixing Strength
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• From the Gaffnian critical point to the incompressible 2/5 quantum Hall state