A Matrix Model for Bilayered Quantum Hall Systems

TL;DR

This paper introduces a matrix model for bilayered quantum Hall systems that reproduces known wave functions and can be extended to multiple layers, providing a new theoretical framework for understanding these complex quantum states.

Contribution

The paper develops a novel matrix model for bilayered quantum Hall fluids that captures various known wave functions and allows for straightforward generalization to multiple layers.

Findings

Reproduces the  wave function for bilayer quantum Hall states.

Successfully derives the  wave function at filling factor 2/5.

Provides a unified matrix framework for multiple-layer quantum Hall systems.

Abstract

We develop a matrix model to describe bilayered quantum Hall fluids for a series of filling factors. Considering two coupling layers, and starting from a corresponding action, we construct its vacuum configuration at \nu=q_iK_{ij}^{-1}q_j, where K_{ij} is a 2\times 2 matrix and q_i is a vector. Our model allows us to reproduce several well-known wave functions. We show that the wave function \Psi_{(m,m,n)} constructed years ago by Yoshioka, MacDonald and Girvin for the fractional quantum Hall effect at filling factor {2\over m+n} and in particular \Psi_{(3,3,1)} at filling {1\over 2} can be obtained from our vacuum configuration. The unpolarized Halperin wave function and especially that for the fractional quantum Hall state at filling factor {2\over 5} can also be recovered from our approach. Generalization to more than 2 layers is straightforward.