Supersymmetry and Models for Two Kinds of Interacting Particles

TL;DR

This paper introduces a supersymmetric extension of Calogero-Sutherland models, providing new Hamiltonians that describe two interacting particle types with potential applications in condensed matter physics.

Contribution

It develops a natural supersymmetric extension of Calogero-Sutherland models using Jacobians in superspaces, leading to novel Hamiltonians with physical interpretations.

Findings

Derived supersymmetric Hamiltonians for two interacting particle types

Connected models to physical systems like semiconductors and tensor interactions

Provided a framework for modeling complex particle interactions

Abstract

We show that Calogero-Sutherland models for interacting particles have a natural supersymmetric extension. For the construction, we use Jacobians which appear in certain superspaces. Some of the resulting Hamiltonians have a direct physics interpretation as models for two kinds of interacting particles. One model may serve to describe interacting electrons in a lower and upper band of a quasi-one-dimensional semiconductor, another model corresponds to two kinds of particles confined to two different spatial directions with an interaction involving tensor forces.