Noncommutativity Parameter and Composite Fermions

TL;DR

This paper explores the noncommutativity parameter in the fractional quantum Hall effect, providing a measurement based on experimental data, and shows the connection between noncommutative geometry and composite fermions, extending previous approaches.

Contribution

It introduces a generalized framework for the noncommutativity parameter , relates it to experimental data, and reveals a broader geometric interpretation of the composite fermion mapping.

Findings

 can be measured using experimental FQHE data.

 can be quantized fractionally or integrally in terms of magnetic length.

The composite fermion mapping has a noncommutative geometric nature.

Abstract

We determine some particular values of the noncommutativity parameter \theta and show that the Murthy-Shankar approach is in fact a particular case of a more general one. Indeed, using the fractional quantum Hall effect (FQHE) experimental data, we give a measurement of \theta. This measurement can be obtained by considering some values of the filling factor \nu and other ingredients, magnetic field B and electron density \rho. Moreover, it is found that \theta can be quantized either fractionally or integrally in terms of the magnetic length l_0 and the quantization is exactly what Murthy and Shankar formulated recently for the FQHE. On the other hand, we show that the mapping of the FQHE in terms of the composite fermion basis has a noncommutative geometry nature and therefore there is a more general way than the Murthy-Shankar method to do this mapping.