Kitaev's Lattice Model and Turaev-Viro TQFTs

TL;DR

This paper demonstrates that Kitaev's lattice model for any complex semisimple Hopf algebra produces the same topological invariants as Turaev-Viro theory and relates excited states to TQFT on surfaces with boundary.

Contribution

It establishes the equivalence between Kitaev's lattice model and Turaev-Viro TQFTs for arbitrary complex semisimple Hopf algebras, extending previous results.

Findings

Kitaev's model matches Turaev-Viro invariants

Excited states correspond to TQFT on surfaces with boundary

Provides a unified framework for topological quantum computation

Abstract

In this paper, we examine Kitaev's lattice model for an arbitrary complex, semisimple Hopf algebra. We prove that this model gives the same topological invariants as Turaev-Viro theory. Using the description of Turaev-Viro theory as an extended TQFT, we prove that the excited states of the Kitaev model correspond to Turaev-Viro theory on a surface with boundary.