Algebraic Approach to Fractional Quantum Hall Effect

TL;DR

This paper develops an algebraic framework to describe the ground state and static response of fractional quantum Hall systems at specific filling factors, revealing universal structure factors in the large N limit.

Contribution

It introduces an algebraic approach to analyze the shape fluctuations of the Fermi surface of composite fermions in fractional quantum Hall states.

Findings

Derived explicit form of the projected static structure factor at large N.

Found the structure factor is independent of the Hamiltonian for certain parameters.

Provided insights into the shape fluctuations of the composite fermion Fermi surface.

Abstract

We construct an algebraic description for the ground state and for the static response of the quantum Hall plateaux with filling factor $\nu=N/(2N+1)$ in the large $N$ limit. By analyzing the algebra of the fluctuations of the shape of the Fermi surface of the composite fermions, we find the explicit form of the projected static structure factor at large $N$ and fixed $z=(2N+1) q\ell_B\sim 1$. When $z<3.8$, the result does not depend on the particular form of the Hamiltonian.