Triviality of a model of particles with point interactions in the thermodynamic limit

TL;DR

This paper demonstrates that a fermionic particle model with point interactions becomes effectively non-interacting in the thermodynamic limit, as the free energy density matches that of free particles despite the interactions.

Contribution

It proves the triviality of a fermionic point interaction model in the thermodynamic limit, showing the interactions vanish at large scales.

Findings

Free energy density matches non-interacting particles

Interaction effects diminish with increasing particle number

Model becomes trivial in the thermodynamic limit

Abstract

We consider a model of fermions interacting via point interactions, defined via a certain weighted Dirichlet form. While for two particles the interaction corresponds to infinite scattering length, the presence of further particles effectively decreases the interaction strength. We show that the model becomes trivial in the thermodynamic limit, in the sense that the free energy density at any given particle density and temperature agrees with the corresponding expression for non-interacting particles.