The few-body universality is not exact for more than three particles

TL;DR

This paper demonstrates analytically that the conjectured universal relation between the ground state energies of three and four bosons, under specific resonance conditions, cannot be exact, challenging previous assumptions about few-body universality.

Contribution

It provides a rigorous proof that the supposed exact universality relation for three and four bosons does not hold, clarifying limitations of the universality conjecture.

Findings

Universal relation between three and four boson energies is not exact.

Analytical proof refutes the conjecture of exact universality.

Highlights limitations of few-body universality in quantum systems.

Abstract

In the literature it is conjectured that the ground state energies of three and four bosons are universally related for all pair-interactions given that two bosons have a zero energy resonance and no negative energy bound states. Here it is proved analytically that such relation cannot be exact.