Ferromagnetism by the generator coordinate Method

The Generator Coordinate Method is applied to construct a boson representation of the energy of a S = 12 ferromagnet near its ground-state. Considering one generator coordinate per lattice site the resulting representation coincides with the one obtained starting from the Dirac-Heisenberg Hamiltonian and using the Holstein-Primakoff transformation, expanded to all orders, inside the physical subspace. On the other hand, introducing generator coordinates to describe only the long-wavelength modes, we obtain a representation which can be consistently expanded until any desired order of approximation.