# Parton construction of particle-hole-conjugate Read-Rezayi parafermion fractional quantum Hall states and beyond

## TL;DR

This paper introduces a parton construction for particle-hole-conjugate Read-Rezayi fractional quantum Hall states, enabling efficient wave function generation and revealing new dualities in their theoretical description.

## Contribution

The authors develop a novel parton framework for anti-RR states, linking them to specific conformal field theories and expanding the ability to model large systems.

## Key findings

- Parton states match anti-RR universality classes.
- Wave functions generated for hundreds of particles.
- Proposed parton sequences describe observed FQH states.

## Abstract

The Read-Rezayi (RR) parafermion states form a series of exotic non-Abelian fractional quantum Hall (FQH) states at filling $\nu = k/(k+2)$. Computationally, the wave functions of these states are prohibitively expensive to generate for large systems. We introduce a series of parton states, denoted "$\bar{2}^{k}1^{k+1}$," and show that they lie in the same universality classes as the particle-hole-conjugate RR ("anti-RR") states. Our analytical results imply that a $(U(1)_{k+1} \times U(2k)_{-1})/(SU(k)_{-2} \times U(1)_{-1})$ coset conformal field theory describes the edge excitations of the $\bar{2}^{k}1^{k+1}$ state, suggesting non-trivial dualities with respect to previously known descriptions. The parton construction allows wave functions in anti-RR phases to be generated for hundreds of particles. We further propose the parton sequence "$\bar{n}\bar{2}^{2}1^{4}$," with $n=1,2,3$, to describe the FQH states observed at $\nu=2+1/2,~2+2/5$ and $2+3/8$.