Simplifying quantum double Hamiltonians using perturbative gadgets

Perturbative gadgets were originally introduced to generate effective k-local interactionsin the low-energy sector of a 2-local Hamiltonian. Extending this idea, we present gadgetswhich are specifically suited for realizing Hamiltonians exhibiting non-abelian anyonicexcitations. At the core of our construction is a perturbative analysis of a widely usedhopping-term Hamiltonian. We show that in the low-energy limit, this Hamiltonian canbe approximated by a certain ordered product of operators. In particular, this providesa simplified realization of Kitaev's quantum double Hamiltonians.

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