SU(m|n) supersymmetric Calogero-Sutherland model confined in harmonic potential

TL;DR

This paper analyzes a supersymmetric SU(m|n) Calogero-Sutherland model confined in a harmonic potential, explicitly constructing the ground state and spectrum, and generalizing previous results to mixed boson-fermion systems.

Contribution

It provides the explicit construction of the ground state wavefunction and energy spectrum for the SU(m|n) supersymmetric Calogero-Sutherland model with harmonic confinement.

Findings

Ground state wavefunction explicitly constructed

Energy spectrum is equally spaced

Results generalize previous bosonic-only models

Abstract

In this work, we study a continuous quantum system of a mixture of bosons and fermions with the supersymmetry SU(m|n). The particles are confined in a harmonic well and interact with each other through the 1/r2 interaction. The ground state wavefunction is constructed explicitly for the most general SU(m|n) case, with the ground state energy given explicitly. The full energy spectrum of excitations in the SU(m|n) model is also equal spaced. In the limiting case where there are no bosons in the system, our results reduce to those obtained previously.