Twisted Kitaev quantum double model as local topological order

TL;DR

This paper analyzes the Twisted Kitaev Quantum Double model using the framework of Local Topological Order, extending its applicability to arbitrary 2D lattices and demonstrating its ground state space as a quantum error-correcting code.

Contribution

It extends the definition of Local Topological Order to arbitrary 2D lattices and characterizes the ground state space via monomial representations.

Findings

The model satisfies all four LTO axioms on any 2D lattice.

The ground state space forms a quantum error-correcting code.

Provides an explicit characterization of the ground state space.

Abstract

We study the Twisted Kitaev Quantum Double model within the framework of Local Topological Order (LTO). We extend its definition to arbitrary 2D lattices, enabling an explicit characterization of the ground state space through the invariant spaces of monomial representations. We reformulate the LTO conditions to include general lattices and prove that the twisted model satisfies all four LTO axioms on any 2D lattice. As a corollary, we show that its ground state space is a quantum error-correcting code.