Low Energy Effective Hamiltonian for the Fractional Quantum Hall Effect

TL;DR

This paper derives a low energy effective Hamiltonian for the fractional quantum Hall effect using symmetry group representations, revealing a similarity to the Heisenberg spin chain and aiding numerical gap analysis.

Contribution

It introduces a novel effective Hamiltonian framework for the fractional quantum Hall effect based on symmetry group irreducible representations.

Findings

Effective Hamiltonian resembles Heisenberg spin chain

Symmetry analysis enables Hilbert space decomposition

Facilitates numerical gap studies in quantum Hall systems

Abstract

A low energy effective Hamiltonian for the fractional quantum Hall effect is obtained by using irreducible representations of the symmetry group. It is found that the model described by the effective Hamiltonian is similar to the Heisenberg spin chain. Symmetries of the effective Hamiltonian are studied in order to decompose the relevant Hilbert space. This decomposition will be useful for further numerical analysis on the gap of the quantum Hall system.