Three fermions in a box at the unitary limit: universality in a lattice model

TL;DR

This study numerically investigates three fermions at unitarity in a lattice model, demonstrating universality and convergence to the zero-range Bethe-Peierls model as the lattice spacing decreases.

Contribution

It provides numerical evidence and analytical insights showing the universality of the zero-range limit for three fermions at unitarity on a lattice.

Findings

No negative energy solutions found.

Rapid convergence to Bethe-Peierls model as lattice spacing decreases.

Universality of zero-range limit established.

Abstract

We consider three fermions with two spin components interacting on a lattice model with an infinite scattering length. Low lying eigenenergies in a cubic box with periodic boundary conditions, and for a zero total momentum, are calculated numerically for decreasing values of the lattice period. The results are compared to the predictions of the zero range Bethe-Peierls model in continuous space, where the interaction is replaced by contact conditions. The numerical computation, combined with analytical arguments, shows the absence of negative energy solution, and a rapid convergence of the lattice model towards the Bethe-Peierls model for a vanishing lattice period. This establishes for this system the universality of the zero interaction range limit.