  We demonstrate the utility of effective Hamilonians for studying strongly
correlated systems, such as quantum spin systems. After defining local relevant
degrees of freedom, the numerical Contractor Renormalization (CORE) method is
applied in two steps:
  (i) building an effective Hamiltonian with longer ranged interactions up to a
certain cut-off using the CORE algorithm and
  (ii) solving this new model numerically on finite clusters by exact
diagonalization and performing finite-size extrapolations to obtain results in
the thermodynamic limit.
  This approach, giving complementary information to analytical treatments of
the CORE Hamiltonian, can be used as a semi-quantitative numerical method to
study frustrated magnets (as the S=1/2 kagome lattice) or doped systems.
