Ferromagnetism and Borromean binding in three-fermion clusters

Area of Science:

• Condensed matter physics
• Quantum mechanics
• Many-body systems

Background:

• Understanding emergent phenomena in quantum systems is crucial.
• Fermionic systems with competing interactions present complex behaviors.
• The formation and stability of few-body bound states are key research areas.

Purpose of the Study:

• To solve the three-particle spin-1/2 fermion problem on a 2D lattice.
• To investigate the binding conditions and stability of trions.
• To explore the system's behavior under varying interaction strengths and total spin.

Main Methods:

• Discretization of the Schrödinger equation in momentum space.
• Analysis of a three-particle system with on-site repulsion and nearest-neighbor attraction.
• Calculation of energies for bound complexes (trions).

Main Results:

• Identified a wide region of instability for spin-1/2 trions, decaying into a singlet pair and a free fermion.
• Attributed spin-1/2 trion instability to wave function node formation.
• Observed Borromean binding for spin-3/2 trions, forming without pre-existing bound pairs.
• Found a transition from spin-1/2 to a ferromagnetic spin-3/2 ground state in the strong coupling limit.

Conclusions:

• The study elucidates the delicate balance governing trion formation and stability.
• Borromean binding in the spin-3/2 sector highlights novel quantum phenomena.
• The observed ground state transition supports theoretical predictions like the Nagaoka theorem.