Free Fermions Behind the Disguise

An invaluable method for probing the physics of a quantum many-body spin system is mapping to noninteracting effective fermions. We find such mappings using only frustration graph G Hamiltonian H, i.e., network anticommutation relations between Pauli terms in H given basis. Specifically, when (even-hole, claw)-free, we construct an explicit free-fermion solution this structure G, even no Jordan–Wigner transformation exists. The generic that it applies any values couplings. This generalizes both classic Lieb–Schultz–Mattis XY model and exact chain recently by Fendley, dubbed “free fermions disguise.” Like Fendley’s original example, operators solve are generally highly nonlinear nonlocal, but can nonetheless be found explicitly transfer operator defined independent sets G. associated single-particle energies calculated roots independence polynomial which guaranteed real result Chudnovsky Seymour. Furthermore, recognizing claw)-free graphs done time, so solvable way efficient. In crucial step proving our result, additionally prove there exists hierarchy commuting conserved charges models whose claw-free only, hence these integrable. Finally, give several example families integrable exists, detailed analysis having 4-body couplings method.