$N$-boson spectrum from a Discrete Scale Invariance

Understand

We present the analysis of the $N$-boson spectrum computed using a soft two-body potential the strength of which has been varied in order to cover an extended range of positive and negative values of the two-body scattering length $a$ close to the unitary limit.

• The spectrum shows a tree structure of two states, one shallow and one deep, attached to the ground-state of the system with one less particle.
• It is governed by an unique universal function, $\Delta(\xi)$, already known in the case of three bosons.
• In the three-particle system the angle $\xi$, determined by the ratio of the two- and three-body binding energies $E_3/E_2=\tan^2\xi$, characterizes the Discrete Scale Invariance of the system.