The partially-filled bosonic E8 quantum Hall state

We study chiral bosonic topological phases constructed from electrons. In addition to a bulk excitation energy gap, these bosonic phases also have a fermion energy gap below which all local excitations in the bulk and on the edge are bosonic even combinations of electrons. We focus on phases that can arise from the short-range entangled E8 quantum Hall state, the bosonic analogue of the filled lowest Landau level of electrons. We present families of long-range entangled bosonic fractional states that "partially fill" the E8 state and are pairwise related by a generalized particle-hole symmetry. We construct exactly solvable coupled-wire model Hamiltonians of these phases and observe the emergence of non-local fermions and gauge theories.