# Paired parton quantum Hall states: a coupled wire construction

## TL;DR

This paper introduces a new family of non-Abelian fractional quantum Hall states at filling 1/6, derived from coupled wire models, supporting Ising-like anyons and connecting to topological insulator surface states.

## Contribution

It proposes a novel paired parton fractional quantum Hall state at filling 1/6, derived from a coupled wire construction, and establishes a new particle-hole symmetry for partons.

## Key findings

- Supports non-Abelian Pfaffian topological order for partons
- Constructs exactly solvable wire models for these states
- Links parton states to 3D fractional topological insulator surfaces

## Abstract

The Pfaffian fractional quantum Hall (FQH) states are incompressible non-Abelian topological fluids present in a half-filled electron Landau level, where there is a balanced population of electrons and holes. They give rise to half-integral quantum Hall plateaus that divide critical transitions between integer quantum Hall (IQH) states. On the other hand, there are Abelian FQH states, such as the Laughlin state, that can be understood using partons, which are fermionic divisions of the electron. In this paper, we propose a new family of incompressible paired parton FQH states at filling $\nu=1/6$ (modulo 1) that emerge from critical transitions between IQH states and Abelian FQH states at filling $\nu=1/3$ (modulo 1). These paired parton states are originated from a half-filled parton Landau level, where there is an equal amount of partons and holes. They generically support Ising-like anyonic quasiparticle excitations and carry non-Abelian Pfaffian topological orders (TO) for partons. We prove the principle existence of these paired parton states using exactly solvable interacting arrays of electronic wires under a magnetic field. Moreover, we establish a new notion of particle-hole (PH) symmetry for partons and relate the PH symmetric parton Pfaffian TO with the gapped symmetric surface TO of a fractional topological insulator in three dimension.