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

TL;DR

This paper proposes a closed-form ground state wave function for the 4/11 fractional quantum Hall state, demonstrating its accuracy through overlaps and correlation functions, and highlights the importance of specific interactions for its incompressibility.

Contribution

A novel closed-form wave function for the 4/11 state is introduced, validated against exact solutions, and shown to require specific interactions for stability.

Findings

High overlap with existing wave functions

Nonzero $V_3$ interaction is crucial

Wave function accurately captures 4/11 state properties

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.