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Spectral degeneracy of hidden free-fermion spin chains

Can a hidden free-fermion spin-chain solution avoid the exponentially growing homogeneous spectral degeneracy of earlier examples? The proposed setting has open boundaries, two compatible Ising-type algebras and generic couplings.

Why it matters and what counts as progress

Why it matters: Removing generic exponential degeneracy would enlarge the usefulness of hidden free-fermion exact solutions.

What counts as progress: Construct an exactly solvable Hamiltonian with controlled generic degeneracy or characterize the couplings where degeneracy returns.

How the problem developed

  1. 14 Dec 2020 · Method [1]

    Samuel J. Elman, Adrian Chapman and Steven T. Flammia Presented graph-based mappings that find hidden free-fermion solutions for spin Hamiltonians beyond the Jordan–Wigner method, including the free-fermions-in-disguise construction.

  2. 2024 · Model family [2]

    Paul Fendley and Balázs Pozsgay Extended free-fermion solutions beyond the Jordan–Wigner paradigm; these earlier examples had exponentially growing homogeneous spectral degeneracies, as later summarized by Pozsgay.

  3. 8 Jun 2026 · Model result [3]

    Balázs Pozsgay Introduced a particular disguised-free-fermion spin-chain model whose spectrum has no exponential degeneracies for generic coupling constants; the preprint describes ChatGPT Pro 5.4 and 5.5 as research assistants.

AI contribution

Sources

  1. Elman, Chapman and Flammia, Free fermions behind the disguise
  2. Fendley and Pozsgay, Free fermions beyond Jordan and Wigner
  3. Balázs Pozsgay, Free fermions in disguise without exponential degeneracies
  4. Pozsgay, free fermions in disguise without exponential degeneracies
  5. Pozsgay, supplemental account of AI and human contributions
Website timeline

Publication dates and editorial changes.