Non-Abelian twist to integer quantum Hall states

Abstract

At a fixed magnetic filling fraction, fractional quantum Hall states may display a plethora of interaction-induced competing phases. Effective Chern-Simons theories have suggested the existence of multiple interaction-induced short-range entangled phases also at integer quantum Hall plateaus. Among these, a bosonic phase has been proposed with edge modes carrying representations based on the ${E}_{8}$ exceptional Lie algebra. Through a theoretical coupled-wire construction, we provide an explicit microscopic model for this ${E}_{8}$ Abelian quantum Hall state, at filling $\ensuremath{\nu}=16$, and discuss how it is intimately related to topological paramagnets in $3+1$ dimensions. Still using coupled wires, we partition the ${E}_{8}$ state into a pair of non-Abelian, long-range entangled states. These two states occur at filling $\ensuremath{\nu}=8$, demonstrating that even topological order may also exist at integer Hall plateaus. These phases are bosonic, carry chiral edge theories with either ${G}_{2}$ or ${F}_{4}$ internal symmetries, and host Fibonacci anyonic excitations in the bulk. This suggests that the $\ensuremath{\nu}=8$ quantum Hall plateau may provide an unexpected platform to realize decoherence-free quantum computation by anyon braiding. We also find that these topological ordered phases are related by a notion of particle-hole conjugation based on the ${E}_{8}$ state that exchanges the ${G}_{2}$ and ${F}_{4}$ Fibonacci states. We argue that these phases can be tracked down by their electric and thermal Hall transport satisfying a distinctive Wiedemann-Franz law $\left({\ensuremath{\kappa}}_{xy}/{\ensuremath{\sigma}}_{xy}\right)/\left[\left({\ensuremath{\pi}}^{2}{k}_{B}^{2}T\right)/3{e}^{2}\right]<1$, even at integer magnetic filling factors.