Iterative methods that operate with the full Hamiltonian matrix in theuntrimmed Hilbert space of a finite system continue to be important tools forthe study of one- and two-dimensional quantum spin models, in particular in thepresence of frustration. To reach sensible system sizes such numericalcalculations heavily depend on the use of symmetries. We describe adivide-and-conquer strategy for implementing translation symmetries of finitespin 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 ineach matrix vector multiplication, and problem dimensions beyond 10^11 becomeaccessible.
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