Frustration-freeness is decidable but unprovable

arXiv:2611.07337v1 Announce Type: new Abstract: The frustration-free property is valuable in quantum many-body systems, which states that its ground states simultaneously minimize all local interaction terms, even when these terms act on overlapping degrees of freedom. Prominent examples include the AKLT model and Kitaev's toric code model, which serve as paradigmatic models of symmetry-protected topological phases and topological order, respectively. A fundamental question is whether a given Hamiltonian is frustration-free for all system sizes. Here we establish two seemingly contradictory results concerning this decision problem. First, we prove that frustration-freeness is decidable for any fixed local Hilbert space dimension.