  In many condensed-matter systems, it is very useful to introduce a
quasi-particle approach, which is based on some sort of linearization around a
suitable background state. In order to be a systematic and controlled
approximation, this linearization should be justified by an expansion into
powers of some small control parameter. Here, we present a method for general
lattice Hamiltonians with large coordination numbers Z >> 1, which is based on
an expansion into powers of 1/Z. In order to demonstrate the generality of our
method, we apply it to various spin systems, as well as the Bose and Fermi
Hubbard model.
