Generalized Quantum Hall Projection Hamiltonians

TL;DR

This paper generalizes the construction of quantum Hall states as zero energy ground states of projection Hamiltonians, extending known models like Laughlin and Moore-Read to new parameters.

Contribution

It introduces a systematic method to find highest density zero energy states for a broader class of quantum Hall projection Hamiltonians.

Findings

Identified new quantum Hall states as zero energy solutions.

Extended the framework for constructing quantum Hall wavefunctions.

Provided explicit examples for various parameters p and g.

Abstract

Certain well known quantum Hall states -- including the Laughlin states, the Moore-Read Pfaffian, and the Read-Rezayi Parafermion states -- can be defined as the unique lowest degree symmetric analytic function that vanishes as at least p powers as some number (g+1) of particles approach the same point. Analogously, these same quantum Hall states can be generated as the exact highest density zero energy state of simple angular momentum projection operators. Following this theme we determine the highest density zero energy state for many other values of p and g.