Heisenberg ferromagnets with single-ion planar anisotropy: a systematic perturbative approach by the Dyson-Maleev transformation

The authors present a perturbative approach to the bosonic equivalent Hamiltonians starting from the Dyson-Maleev (DM) transformation for the easy-plane Heisenberg ferromagnet with single-ion anisotropy. No one else has used the DM transformation for this model, because not only are non-Hermitian interaction potentials obtained as usual, but even the bilinear part of the Hamiltonian acquires a non-Hermitian contribution from the normal ordering of the interaction potentials; this fact obviously prevents the customary diagonalisation by a Bogoliubov transformation. The authors show that this problem can be overcome; so even for the model they consider, one has the relevant advantages of the DM transformation, namely a finite number of interaction potentials, while other transformations, such as the Holstein-Primakoff transformation (HP), give an infinite number of potentials. The same magnon excitation spectrum is obtained whatever bosonic realisation of the spin operators is adopted, provided all contributions of the same weight with respect to the expansion parameters (the anisotropy and the inverse of the spin S) are picked out. Moreover, starting from the DM transformation the present state of the art can be improved somewhat, taking advantage of the finite number of interaction potentials.