Chiral topologically ordered states on a lattice from vertex operator algebra

Abstract

I will describe a certain class of short-range correlated pure states of 2d lattice systems naturally associated with a unitary rational vertex operator algebra. I will argue that such states realize the chiral topological order associated with this vertex algebra. The construction provides a natural way to insert anyons and compute certain topological invariants. It also gives candidates for bosonic states in non-trivial invertible phases, including the E_8 phase.