  We examine a parametric cycle in the N-body Lieb-Liniger model that starts
from the free system and goes through Tonks-Girardeau and super-Tonks-Girardeau
regimes and comes back to the free system. We show the existence of exotic
quantum holonomy, whose detailed workings are analysed with the specific sample
of two- and three body systems. The classification of eigenstates based on
clustering structure naturally emerges from the analysis.
