  Iterative methods that operate with the full Hamiltonian matrix in the
untrimmed Hilbert space of a finite system continue to be important tools for
the study of one- and two-dimensional quantum spin models, in particular in the
presence of frustration. To reach sensible system sizes such numerical
calculations heavily depend on the use of symmetries. We describe a
divide-and-conquer strategy for implementing translation symmetries of finite
spin clusters, which efficiently uses and extends the "sublattice coding" of H.
Q. Lin. With our method, the Hamiltonian matrix can be generated on-the-fly in
each matrix vector multiplication, and problem dimensions beyond 10^11 become
accessible.
