Defects and excitations in the Kitaev model

TL;DR

This paper develops a generalized Kitaev model incorporating defects via Hopf algebra twists, linking it to Turaev-Viro TQFTs, and analyzes how excitations behave and can be manipulated within this framework.

Contribution

It introduces a method to construct Kitaev models with defects using Hopf algebra cocycles and derives conditions for excitations based on Turaev-Viro theories.

Findings

Defects are modeled using twists and 2-cocycles of Hopf algebras.

Excitations satisfy conditions derived from Turaev-Viro TQFTs.

Transparent defects can be removed, reducing to the defect-free Kitaev model.

Abstract

We construct a Kitaev model with defects using twists or 2-cocycles of semi-simple, finite-dimensional Hopf algebras as defect data. This data is derived by applying Tannaka duality to Turaev-Viro topological quantum field theories with defects. From this we also derive additional conditions for moving, fusing and braiding excitations in the Kitaev model with defects. We give a description of excitations in the Kitaev model and show that they satisfy conditions we derive from Turaev-Viro topological quantum field theories with defects. Assigning trivial defect data one obtains transparent defects and we show that they can be removed, yielding the Kitaev model without defects.