Level crossing in the three-body problem for strongly interacting fermions in a harmonic trap

TL;DR

This paper solves the three-fermion problem in a harmonic trap across a Feshbach resonance, revealing energy level crossings and symmetry changes that suggest possible phase transitions in many-body systems.

Contribution

It provides an exact solution for three strongly interacting fermions in a harmonic trap and analyzes spectral features indicating phase transition potential.

Findings

Three-fermion spectrum compared with two-body case

Energy level crossing in the ground state observed

Symmetry change in wave function suggests phase transition

Abstract

We present a solution of the three-fermion problem in a harmonic potential across a Feshbach resonance. We compare the spectrum with that of the two-body problem and show that it is energetically unfavorable for the three fermions to occupy one lattice site rather than two. We also demonstrate the existence of an energy level crossing in the ground state with a symmetry change of its wave function, suggesting the possibility of a phase transition for the corresponding many-body case.