Analysis shows degeneracy limits for ground states in local Hamiltonians, suggesting constraints under local perturbations.
If a local Hamiltonian eigenstate is mapped to another state by local operators commuting with the Hamiltonian terms, the latter is also an eigenstate. This basic observation implies a no-go result for both being a unique ground state and having a degeneracy protected against local perturbations.
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José Garre-Rubio (2025) studied this question.
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