Jain States in a Matrix Theory of the Quantum Hall Effect

TL;DR

This paper introduces a matrix gauge theory extending noncommutative models to describe quantum Hall states, including Jain states, with a connection to composite fermions and potential for modeling fractional Hall effects.

Contribution

It presents a novel Maxwell-Chern-Simons matrix gauge theory that generalizes previous noncommutative models and captures Jain hierarchical states through gauge invariance.

Findings

Matrix ground states correspond to Laughlin and Jain states

The theory reduces to Calogero interaction in commuting matrix limit

Provides an improved effective model for fractional quantum Hall effect

Abstract

The U(N) Maxwell-Chern-Simons matrix gauge theory is proposed as an extension of Susskind's noncommutative approach. The theory describes D0-branes, nonrelativistic particles with matrix coordinates and gauge symmetry, that realize a matrix generalization of the quantum Hall effect. Matrix ground states obtained by suitable projections of higher Landau levels are found to be in one-to-one correspondence with the expected Laughlin and Jain hierarchical states. The Jain composite-fermion construction follows by gauge invariance via the Gauss law constraint. In the limit of commuting, ``normal'' matrices the theory reduces to eigenvalue coordinates that describe realistic electrons with Calogero interaction. The Maxwell-Chern-Simons matrix theory improves earlier noncommutative approaches and could provide another effective theory of the fractional Hall effect.