A simple mechanism for unstable degeneracies in local Hamiltonians

2025/06/03 by Jose Garre Rubio, Rubio, Jose Garre
Engineering · Mathematics · Physics and Astronomy · #Control and Stability of Dynamical Systems #FOS: Physical sciences #Quantum Physics (quant-ph) #Quantum chaos and dynamical systems #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.2506.03228

openalex publication_date 2025/06/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Citations

• W state is not the unique ground state of any local Hamiltonian

Related

• Degenerate subspace localization and local symmetries
• State Engineering of Unsteerable Hamiltonians
• MPS Stability and the Intersection Property
• Generic Local Hamiltonians are Gapless
• Eigenvalue sensitivity from eigenstate geometry near and beyond arbitrary-order exceptional points