# A non-Abelian twist to integer quantum Hall states

## TL;DR

This paper constructs novel strongly correlated integer quantum Hall states using a coupled wire model, revealing violations of the Wiedemann-Franz law and introducing new topological phases with non-Abelian anyons and Fibonacci excitations.

## Contribution

It introduces a new theoretical framework for integer quantum Hall states supporting non-Abelian anyons and explores their topological and edge properties.

## Key findings

- Supports electric and thermal Hall transport violating Wiedemann-Franz law
- Proposes a new Abelian incompressible fluid at filling ν=16 with E8 edge theory
- Identifies non-Abelian quantum Hall states at ν=8 with Fibonacci anyons

## Abstract

Through a theoretical coupled wire model, we construct strongly correlated electronic \emph{integer} quantum Hall states. As a distinguishing feature, these states support electric and thermal Hall transport violating the Wiedemann-Franz law as $\left(\kappa_{xy}/\sigma_{xy}\right)/\left[\left(\pi^{2}k_{B}^{2}T\right)/3e^{2}\right]<1$.We propose a new Abelian incompressible fluid at filling $\nu=16$ that supports a bosonic chiral $(E_{8})_{1}$ conformal field theory at the edge and is intimately related to topological paramagnets in (3+1)D. We further show that this topological phase can be partitioned into two non-Abelian quantum Hall states at filling $\nu=8$, each carrying bosonic chiral $(G_{2})_{1}$ or $(F_{4})_{1}$ edge theories, and hosting Fibonacci anyonic excitations in the bulk. Finally, we discover a new notion of particle-hole conjugation based on the $E_{8}$ state that relates the $G_{2}$ and $F_{4}$ Fibonacci states.