A non-Abelian twist to integer quantum Hall states

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 $\left(κ_{xy}/σ_{xy}\right)/\left[\left(π^{2}k_{B}^{2}T\right)/3e^{2}\right]<1$.We propose a new Abelian incompressible fluid at filling $ν=16$ 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 $ν=8$, 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.