Eur. Phys. J. Plus (2017) 132: 93
https://doi.org/10.1140/epjp/i2017-11362-7

Regular Article

N=2 supersymmetric quantum mechanics of N Lieb-Liniger-Yang bosons on a line

¹ Departamento de Fisica Fundamental, University of Salamanca, Salamanca, Spain
² Facultad Tecnológica, Universidad Distrital Francisco José de Caldas, Bogotá, Colombia

^* e-mail: guilarte@usal.es

Received: 27 September 2016
Accepted: 22 January 2017
Published online: 22 February 2017

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 Pösch-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 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.