Exact Results for Spin and Charge Dynamics of Electrons with Supersymmetry

TL;DR

This paper provides exact analytical results for the spin and charge dynamics in a supersymmetric t-J model with long-range interactions, revealing quadratic energy dependence and explaining spin-charge separation.

Contribution

It introduces a simple explanation for spin-charge separation using a first-quantized representation and derives a key identity for permutation properties of SU(ν) wave functions.

Findings

Quadratic dependence of excitation spectra on spin and charge currents.

Explanation of spin-charge separation in supersymmetric models.

Derivation of permutation property identities for SU(ν) wave functions.

Abstract

Excitation spectra in the SU($\nu +1$,1) supersymmetric t-J model with long-range exchange and transfer has quadratic dependence on spin and charge currents for all energies. After brief review on the supersymmetry, this paper gives a simple explanation for the spin-charge separation on the basis of a first-quantized representation. A useful identity is derived on permutation properties of SU($\nu$) Jastrow-type wave functions, which constitute the ground states for a class of 1/$r^2$ interaction models.