Free Fermions in Disguise without Exponential Degeneracies

An existence question settled by exhibiting an object, not a general theorem: one model in the family has no exponential degeneracies for generic couplings, and nothing here says which others do. The route is worth recording because it is not the one anyone was looking down. The author had tried and failed to find such a model directly. It surfaced instead from an unrelated classification of medium-range spin chains, where the AI's computations produced a list of integrable Hamiltonians and one of them combined two terms of a standard XY chain with two of Fendley's FFD model, a combination nobody had considered. The author noticed it in the list; the rest followed from asking the model a sequence of increasingly specific questions.

An existence question settled by exhibiting an object, not a general theorem: one model in the family has no exponential degeneracies for generic couplings, and nothing here says which others do. The route is worth recording because it is not the one anyone was looking down. The author had tried and failed to find such a model directly. It surfaced instead from an unrelated classification of medium-range spin chains, where the AI's computations produced a list of integrable Hamiltonians and one of them combined two terms of a standard XY chain with two of Fendley's FFD model, a combination nobody had considered. The author noticed it in the list; the rest followed from asking the model a sequence of increasingly specific questions.