Interacting quantum Hall states at integer filling with a non-Abelian twist: a coupled wire description

We construct a theoretical coupled wire model that describes new many-body interacting quantum Hall states at integer filling. The strongly-correlated states support exotic electric and thermal Hall transport that violate the Wiedemann-Franz law ν/c=(σ_xy/κ_xy)[π²k_B²/(3e²)]T>1. We focus on strongly-paired states where combinations of pairs of electrons form the fundamental interacting constituents. These bosonic combinations associate to a Kac-Moody current algebra, which is removed from low-energy by the interaction in the 2+1D bulk but is left behind along the 1+1D boundary. We propose a new quantum Hall state at filling ν=16 that supports a bosonic chiral E₈ edge current algebra at level 1 and is intimately related to the topological paramagnets in 3+1D. This topological state can be partitioned into two quantum Hall states at filling ν=8, each carries a bosonic chiral G₂ or F₄ edge current algebra at level 1 and hosts non-Abelian Fibonacci anyonic excitations in the bulk. Moreover, we discover a new notion of particle-hole conjugation, based on the E₈ bosons, that switches between the G₂ and F₄ states.