Chiral topologically ordered states on a lattice from vertex operator algebras

TL;DR

This paper introduces a new class of lattice states exhibiting chiral topological order linked to vertex operator algebras, with potential applications in quantum computing and phases of matter.

Contribution

It constructs and analyzes pure lattice states with topological order derived from vertex operator algebras, including methods to insert anyons and compute invariants.

Findings

States are well-defined in the thermodynamic limit

States exhibit exponential decay of correlations

Provides candidates for bosonic states in non-trivial invertible phases

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.