Twisted index theory on orbifold symmetric products and the fractional quantum Hall effect

TL;DR

This paper extends a noncommutative geometry model of the fractional quantum Hall effect to orbifold symmetric products, preserving quantization properties and enabling new representations and wave functions.

Contribution

It introduces a novel extension of the model to orbifold symmetric products, maintaining quantization and enabling composite fermion and anyon representations.

Findings

Quantization of Hall conductance at fractional orbifold Euler characteristics

Potential for Laughlin type wave functions

Supports composite fermion and anyon representations

Abstract

We extend the noncommutative geometry model of the fractional quantum Hall effect, previously developed by Mathai and the first author, to orbifold symmetric products. It retains the same properties of quantization of the Hall conductance at integer multiples of the fractional Satake orbifold Euler characteristics. We show that it also allows for interesting composite fermions and anyon representations, and possibly for Laughlin type wave functions.