Quantum Hall Ground States and Regular Graphs

TL;DR

This paper links quantum Hall ground states to regular graphs, introducing a graph-based approach to construct trial states with specific clustering properties, and demonstrates their realization as zero-energy states in a modified Hamiltonian model.

Contribution

It develops a novel graph-based ansatz for quantum Hall states, connecting uniform states on the sphere to superpositions of regular graphs and their local properties.

Findings

Uniform states on the sphere are superpositions of regular graphs.

Constructed trial states exhibit $(k,r)$ clustering properties.

A subclass of states is realizable as zero-energy states of a modified Hamiltonian.

Abstract

We show that every uniform state on the sphere is essentially a superposition of regular graphs. In addition, we develop a graph-based ansatz to construct trial FHQ ground states sharing the local properties of Jack polynomials. In particular, our graphic states have the $(k,r)$ clustering property. Moreover, a subclass of the construction is realizable as the densest zero-energy state of a model that modifies the projection Hamiltonian.