Ferromagnetism and Borromean binding in three-fermion clusters

A three-particle spin-1/2 fermion problem with on-site repulsion and nearest-neighbor attraction is solved on the two-dimensional square lattice by discretizing a Schroedinger equation in momentum space. Energies of bound complexes (trions) and their binding conditions are obtained. For total spin S = 1/2, a wide region of trion instability toward decaying into a stable singlet pair plus a free fermion is identified. The instability is attributed to the formation of a wave function node upon addition of the third fermion. In the S = 3/2 sector, trions are found to form before triplet pairs indicating Borromean binding. In the strong repulsion, strong attraction limit the system transitions from an S = 1/2 ground state to a ferromagnetic S = 3/2 ground state in agreement with the Nagaoka theorem for a four-site plaquette.