Comment on ‘‘t/U expansion for the Hubbard model’’

It is shown that a unitary transformation which eliminates the terms which couple states with different numbers of doubly occupied sites in the Hubbard model, proposed recently by MacDonald, Girvin, and Yoshioka, is conceptually equivalent to a canonical perturbation expansion, derived over a decade ago. In the half-filled case, the latter method gives an effective Hamiltonian in which many-body interactions result from even numbers of interconfigurational transitions. It is argued that it is hard to conclude anything about the nature of the ground state from the energies of the Néel state and various valence-bond states, as calculated by MacDonald et al., due to the importance of quantum fluctuations in a two-dimensional lattice.