For any finite group, states with zero energy density in a contractible region are locally indistinguishable in Kitaev's quantum double model, which makes the model a quantum error-correcting code.
The complete set of infinite volume ground states for Kitaev’s Abelian quantum double models.Communications in Mathematical Physics, 357(1):125–157, 2018
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Kitaev's quantum double model as an error correcting code
For any finite group, states with zero energy density in a contractible region are locally indistinguishable in Kitaev's quantum double model, which makes the model a quantum error-correcting code.