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arXiv · 2011.04495

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

Sahana Das·Sudipto Das·Sudhansu S. Mandal
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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.

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Sahana Das, Sudipto Das, Sudhansu S. Mandal. 2021-06-21. Unconventional Filling Factor 4/11: A Closed-Form Ground State Wave Function. https://doi.org/10.1103/physrevb.103.075304

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