Exciton in Matrix Formulation of Quantum Hall Effect

TL;DR

This paper models the quantum Hall effect using a two-component matrix approach to describe excitons, deriving their energy corrections and dispersion relations through quantum and classical analyses.

Contribution

It introduces a novel two-component matrix model for quantum Hall excitons, extending previous constraints to include exciton solutions and quantum state analysis.

Findings

Derived classical exciton solutions with quasi-electron and quasi-hole excitations.

Quantized the constraint condition and identified physical quantum states.

Estimated exciton energy corrections and obtained dispersion relations.

Abstract

The quantum Hall effect is studied by introducing two different matrix variables for electrons and holes, having Chern-Simons type interactions. By generalizing the constraint condition proposed by Susskind to realize the Pauli's exclusion principle in this two component matrix model, the classical exciton solution having excitation of both quasi-electron and quasi-hole is obtained. The constraint condition is also solved quantum mechanically in the infinite-sized matrix case, giving the examples of the physical states. Using these quantum states, the corrections of the exciton energy, coming from the noncommutativity of space (Pauli principle) and from the quantum effects of the background state, are estimated in the lowest order perturbation expansion. As a result, the dispersion relation of exciton is obtained.