A Matrix Model for Fractional Quantum Hall States

TL;DR

This paper introduces a matrix model for fractional quantum Hall states that extends beyond Laughlin theory, capturing a broader class of observable FQH states including those in the Haldane hierarchy.

Contribution

It develops a matrix model for FQH states at specific filling factors, encompassing the Haldane hierarchy and recovering Laughlin states in a certain limit.

Findings

Model captures FQH states like 2/3, 2/5

Extends beyond Laughlin to hierarchy states

Recovers Laughlin series in a specific limit

Abstract

We have developed a matrix model for FQH states at filling factor \nu_{k_1k_2} going beyond the Laughlin theory. To illustrate our idea, we have considered an FQH system of a finite number N=(N_{1}+N_{2}) of electrons with filling factor \nu_{k_{1}k_{2}} = \nu_{p_{1}p_{2}}=\frac{p_{2}}{p_{1}p_{2}-1}; p_{1} is an odd integer and p_{2} is an even integer. The \nu_{p_{1}p_{2}} series corresponds just to the level two of the Haldane hierarchy; it recovers the Laughlin series \nu_{p_{1}} =\frac{1}{p_{1}} by going to the limit p_{2} large and contains several observable FQH states such as \nu = 2/3, 2/5, >....