Dynamical supersymmetry on the XXX spin chain

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.