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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 Landaulevel of the composite fermions whose correlations resemble with that ofelectrons in the ground state of two-body Haldane pseudo-potential of relativeangular momentum 3, $V_3$. We here propose a closed-form ground state wavefunction for $V_3$ at 1/3 filling factor. We successfully compare it with theexact wave function for the systems with a few electrons, by calculating theirmutual overlap, pair-correlation function, and entanglement spectra. Bynumerical exact diagonalization for a few electron systems, we find a window ofnonzero $V_3$ is essential together with $V_1$ for being 4/11 stateincompressible. The constructed wave function for 4/11 state using thisproposed wave function has satisfactorily high overlap with the previouslystudied composite-fermion-diagonalized ground state wave function.

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