Efficient iterative diagonalization of the Bose-Hubbard model for ultracold bosons in a periodic optical trap

► Exact solution of the Bose-Hubbard model is possible by full-CI techniques. ► Davidson's technique for finding eigenvectors are preferred. ► It is imperative to let the Hamiltonian act directly on the trial vector. ► Restricted site occupations can simplify the calculation without loss of accuracy.