English

A simple mechanism for unstable degeneracies in local Hamiltonians

Quantum Physics 2025-10-31 v2

Abstract

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.

Keywords

Cite

@article{arxiv.2506.03228,
  title  = {A simple mechanism for unstable degeneracies in local Hamiltonians},
  author = {Jose Garre Rubio},
  journal= {arXiv preprint arXiv:2506.03228},
  year   = {2025}
}

Comments

1 page, 0 figures. Was this known or written somewhere? Comments are welcome. v2: Improved explanation and proof of instability corrected