Hamiltonian Description of Composite Fermions: Aftermath

TL;DR

This paper extends the low-distance theory of composite fermions to all distances, clarifying their physical binding, constraints, and observable properties, resulting in a consistent and appealing theoretical framework.

Contribution

It provides a minimal extension of the composite fermion theory to all distances, clarifying the physical interpretation and the role of constraints.

Findings

The theory is mathematically consistent.

Electron-vortex binding is clearly demonstrated.

Constraints ensure compressibility at ν=1/2.

Abstract

The Lowest Landau Level (LLL), long distance theory of Composite Fermions (CF) developed by Murthy and myself is minimally extended to all distances, guided by very general principles. The resulting theory is mathematically consistent, and physically appealing: we clearly see the electron and the vortices binding to form the CF. The meaning of the constraints, their role in ensuring compressibility of dipolar objects at $\nu =1/2$, and the observability of dipoles are clarified.