Free fermions behind the disguise

Understand

An invaluable method for probing the physics of a quantum many-body spin system is a mapping to noninteracting effective fermions.

• We find such mappings using only the frustration graph $G$ of a Hamiltonian $H$, i.e., the network of anticommutation relations between the Pauli terms in $H$ in a given basis.
• Specifically, when $G$ is (even-hole, claw)-free, we construct an explicit free-fermion solution for $H$ using only this structure of $G$, even when no Jordan-Wigner transformation exists.
• The solution method is generic in that it applies for any values of the couplings.