Chern-Simons Theory and Dynamics of Composite Fermions

TL;DR

This paper introduces a (4+1)D Chern-Simons field theory to describe the fractional quantum Hall effect, revealing that composite fermions have a nontrivial momentum space topology and follow symplectic dynamics, leading to accurate predictions of Hall conductance.

Contribution

It presents a novel higher-dimensional Chern-Simons framework for the fractional quantum Hall effect, emphasizing the topological and dynamical properties of composite fermions.

Findings

Composite fermions reside on a momentum manifold with nonzero Chern number.

The momentum manifold exhibits uniformly distributed Berry curvature.

The dynamics of composite fermions are symplectic, not Newtonian.

Abstract

We propose a (4+1) dimensional Chern-Simons field theoretical description of the fractional quantum Hall effect. It suggests that composite fermions reside on a momentum manifold with a nonzero Chern number. Based on derivations from microscopic wave functions, we further show that the momentum manifold has a uniformly distributed Berry curvature. As a result, composite fermions do not follow the ordinary Newtonian dynamics as commonly believed, but the more general symplectic one. For a Landau level with the particle-hole symmetry, the theory correctly predicts its Hall conductance at half-filling as well as the symmetry between an electron filling fraction and its hole counterpart.