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

TL;DR

This paper demonstrates how Jack states, which are exact ground states of certain many-body interactions, can emerge from two-body Coulomb interactions in fractional quantum Hall systems, with implications for realistic materials.

Contribution

It shows numerically that Jack states can arise from suitable two-body pseudopotentials, providing a link between idealized models and realistic Coulomb interactions in quantum Hall systems.

Findings

Jack states emerge from tailored two-body pseudopotentials.

A simple empirical formula for optimal pseudopotentials is identified.

Potential realization of Jack states in real materials like GaAs and graphene.

Abstract

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.