Taking the square root of the discrete 1/r² model

Abstract

We exhibit a factorization of the exactly solvable discrete 1/r² exchange Heisenberg model. We express the Hamiltonian of the model on a lattice of L sites, as a sum over the squares of L operators in eight distinct ways, using the eight generators of the SU(3) group, and demonstrate that each of the 8 L operators annihilate the Gutzwiller wave function. The wave function is thus proven to be the exact ground state of the 1/r² model, and we also provide a scheme for the construction of an infinite number of Hamiltonians for which it is the ground state.