The Anatomy of Abelian and Non-Abelian Fractional Quantum Hall States

TL;DR

This paper uncovers new symmetries and recursive relations in Abelian and Non-Abelian Fractional Quantum Hall states, enabling efficient approximations with high overlaps and eliminating the need for diagonalization.

Contribution

It introduces a novel set of symmetries and a recursion formula for FQH state coefficients, improving state approximation methods.

Findings

Derived a recursion formula for FQH state coefficients.

Built high-overlap approximations using reduced Hilbert space.

Removed the need for diagonalization in coefficient calculations.

Abstract

We deduce a new set of symmetries and relations between the coefficients of the expansion of Abelian and Non-Abelian Fractional Quantum Hall (FQH) states in free (bosonic or fermionic) many-body states. Our rules allow to build an approximation of a FQH model state with an overlap increasing with growing system size (that may sometimes reach unity!) while using a fraction of the original Hilbert space. We prove these symmetries by deriving a previously unknown recursion formula for all the coefficients of the Slater expansion of the Laughlin, Read Rezayi and many other states (all Jacks multiplied by Vandermonde determinants), which completely removes the current need for diagonalization procedures.