N=2 supersymmetric quantum mechanics of N Lieb-Liniger-Yang bosons on a line
Departamento de Fisica Fundamental, University of Salamanca, Salamanca, Spain
2 Facultad Tecnológica, Universidad Distrital Francisco José de Caldas, Bogotá, Colombia
* e-mail: firstname.lastname@example.org
Accepted: 22 January 2017
Published online: 22 February 2017
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.
© Società Italiana di Fisica and Springer-Verlag Berlin Heidelberg, 2017