Chiral topologically ordered states on a lattice from vertex operator algebras

Abstract

We propose a class of pure states of two-dimensional lattice systems realizing topological order associated with unitary rational vertex operator algebras. We show that the states are well-defined in the thermodynamic limit and have exponential decay of correlations. 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.

arXiv comment25 pages, 9 figures; V2: Proposition D.1 and the last paragraph of C.2.1 fixed, typos corrected