Dynamical supersymmetry on the XXX spin chain

TL;DR

This paper demonstrates that the XXX spin chain model exhibits N=2 dynamical supersymmetry, connecting supercharges with the Hamiltonian and exploring applications to models with magnetic impurities.

Contribution

It introduces a novel realization of dynamical supersymmetry in the XXX model using Jordan-Wigner fermions and analyzes its implications for models with magnetic impurities.

Findings

Supercharges generate the XXX Hamiltonian with magnetic field.

Length-changing supercharges are interpreted in the spinon basis.

Application to models with magnetic impurities via Bethe-ansatz.

Abstract

We show the XXX model has the N = 2 dynamical supersymmetry. Using the supercharges defined by the Jordan-Wigner fermions, it was found that the anti-commutation relation of the supercharges gives the Hamiltonian of the XXX model with magnetic field. In order to compare the length-change supercharges with the conventional ones, we interpreted their actions in the spinon basis. In the last part of this paper, we propose the application of the dynamical supersymmetry to the models with magnetic impurities through the Bethe-ansatz analysis.