On a C*-Diagonal Generated by the Toric Code

TL;DR

This paper investigates a specific abelian sub-C*-algebra within the CAR algebra generated by the toric code's operators, demonstrating its equivalence to the canonical diagonal of the CAR algebra.

Contribution

It establishes that the abelian sub-C*-algebra generated by the toric code operators is a C*-diagonal equivalent to the CAR algebra's canonical diagonal.

Findings

The sub-C*-algebra is a C*-diagonal.

It is equivalent to the canonical diagonal of the CAR algebra.

Provides insight into the algebraic structure of the toric code operators.

Abstract

We study the abelian sub-C*-algebra of the CAR algebra generated by the start and face opertors of Kitaev's toric code. We show that it is a C*-diagonal equivalent to the canonical diagonal of the CAR algebra.