Semiclassical Droplet States in Matrix Quantum Hall Effect

TL;DR

This paper derives semiclassical ground state solutions in Maxwell-Chern-Simons matrix theory that model fractional quantum Hall states, supporting the theory as an effective description of the phenomenon.

Contribution

It provides explicit semiclassical solutions realizing Jain composite-fermion states within matrix theory, with a detailed analysis of the degeneracy constraint.

Findings

Density profiles are piecewise constant, matching phenomenological wave functions.

The matrix theory effectively models fractional quantum Hall states.

A gauge-invariant form of the degeneracy constraint is derived and interpreted.

Abstract

We derive semiclassical ground state solutions that correspond to the quantum Hall states earlier found in the Maxwell-Chern-Simons matrix theory. They realize the Jain composite-fermion construction and their density is piecewise constant as that of phenomenological wave functions. These results support the matrix theory as a possible effective theory of the fractional Hall effect. A crucial role is played by the constraint limiting the degeneracy of matrix states: we find its explicit gauge invariant form and clarify its physical interpretation.