Reflection Positivity in Spin Space for the Heisenberg Model, the Kondo Hamiltonian and the Kondo Lattice

Abstract

In this article we discuss the reflection positivity in spinspace for the Heisenberg model and the Kondo Hamiltonian. We show thatthe ground state is unique for J≠0 where J is the strength of theexchange interaction in the Heisenberg model or the exchange couplingbetween the localized spins and conduction electrons in the Kondo model.We introduce the Coulomb interaction U>0 between the conductionlectrons for the Kondo Hamiltonian to show the uniqueness of the groundstate. We write the Hamiltonian in terms of fermions to express the exchangeinteractions and impose constraints. We employ the Lagrange-multipliermethod to deal with the constraints in this work.