Quantum holonomy in Lieb-Liniger model

TL;DR

This paper investigates quantum holonomy phenomena in the Lieb-Liniger model, revealing exotic eigenstate transformations during a parameter cycle through different interaction regimes, with detailed analysis on small systems.

Contribution

It introduces the concept of quantum holonomy in the Lieb-Liniger model and classifies eigenstates based on clustering structures during a parameter cycle.

Findings

Existence of exotic quantum holonomy in the model

Eigenstate classification based on clustering structures

Analysis demonstrated on two- and three-body systems

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.