Emergence of Jack ground states from two-body pseudopotentials in fractional quantum Hall systems

The family of "Jack states" related to antisymmetric Jack polynomials are the exact zero-energy ground states of particular model short-range {\em many-body} repulsive interactions, defined by a few non-vanishing leading pseudopotentials. Some Jack states are known or anticipated to accurately describe many-electron incompressible ground states emergent from the {\em two-body} Coulomb repulsion in fractional quantum Hall effect. By extensive numerical diagonalization we demonstrate emergence of Jack states from suitable pair interactions. We find empirically a simple formula for the optimal two-body pseudopotentials for the series of most prominent Jack states generated by {\em contact} many-body repulsion. Furthermore, we seek realization of arbitrary Jack states in realistic quantum Hall systems with Coulomb interaction, i.e., in partially filled lowest and excited Landau levels in quasi-two-dimensional layers of conventional semiconductors like GaAs or in graphene.