Abstract
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.
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