{\cal N}=2 Supersymmetric quantum mechanics of N Lieb-Liniger-Yang bosons on a line

TL;DR

This paper develops an ${ m N}=2$ supersymmetric extension of the Lieb-Liniger-Yang model for bosons on a line, analyzing the interplay between integrability, supersymmetry, and ground state properties in different regimes.

Contribution

It introduces a supersymmetric generalization of the Lieb-Liniger-Yang system and explores its ground state structure and supersymmetry breaking in both few-body and many-body limits.

Findings

Supersymmetric extension maintains integrability in certain regimes.

Ground state analysis reveals conditions for spontaneous supersymmetry breaking.

Connections established between supersymmetric quantum mechanics and many-body integrable systems.

Abstract

A supersymmetric generalization of the Lieb-Liniger-Yang dynamics governing $N$ massive bosons moving on a line with delta interactions among them at coinciding points is developed. The analysis of the delicate balance between integrability and supersymmetry, starting from the exactly solvable non supersymmetric LLY system, is one of the paper main concerns. Two extreme regimes of the $N$ parameter are explored: 1) For few bosons we fall in the realm of supersymmetric quantum mechanics with a short number of degrees of freedom, e.g., the SUSY P$\ddot{\rm o}$sch-Teller potentials if $N=1$. 2) For large $N$ we deal with supersymmetric extensions of many body systems in the thermodynamic limit akin, e.g., to the supersymmetric Calogero-Sutherland systems. Emphasis will be put in the investigation of the ground state structure of these quantum mechanical systems enjoying ${\cal N}=2$ extended supersymmetry without spoiling integrability. The decision about wether or not supersymmetry is spontaneously broken, a central question in SUSY quantum mechanics determined from the ground state structure, is another goal of the paper.