• Corpus ID: 234790335

A Note on the Second Spectral Gap Incompleteness Theorem

@inproceedings{Cubitt2021ANO,
  title={A Note on the Second Spectral Gap Incompleteness Theorem},
  author={Toby S. Cubitt},
  year={2021}
}
Pick a formal system. Any formal system. Whatever your favourite formal system is, as long as it’s capable of reasoning about elementary arithmetic. The First Spectral Gap Incompleteness Theorem of [CPGW15] proved that there exist Hamiltonians whose spectral gap is independent of that system: your formal system is incapable of proving that the Hamiltonian is gapped, and equally incapable of proving that it’s gapless. In this note, I prove the Second Spectral Gap Incompleteness Theorem: I show… 
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