Unconventional filling factor of 4/11: A closed-form ground-state wave function

Abstract

The ground state at 4/11 filling factor is very well understood, Mukherjee et al. [Phys. Rev. Lett. 112, 016801 (2014)] in terms of the 1/3-filled second effective Landau level of the composite fermions whose correlations resemble that of electrons in the ground state of a 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 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 the 4/11 state using this proposed wave function has satisfactorily high overlap with previously studied composite-fermion-diagonalized ground-state wave function.