A minimal integer quantum Hall state with an emergent super-symmetric edge and its fractional descendants

We present the theory of a short-range entangled quantum Hall state at filling number ν=4. The topological state is constructed by many-body interacting electrons in a coupled-wire model. There is no adiabatic path connecting it with conventional integer quantum Hall states because its thermal Hall conductance is characterized by the unconventional chiral central charge c=12. The conformal field theory SO(24)₁ that describes the gapless boundary edge has an emergent super-symmetry. It is the super-symmetric extension of the bosonic E₈ Wess-Zumino-Witten theory, and its integral vertex excitations on the edge occupy a unimodular lattice at dimension 12. In addition, we present the theories of a family of long-range entangled fractional quantum Hall states that partially fill the SO(24)₁ state. All fractional descendants in the family carry emergent super-symmetric edge theories and are pairwise related by a generalized notion of particle-hole conjugation.