  The similarity renormalization group (SRG) has been successfully applied to
soften interactions for ab initio nuclear calculations. In almost all practical
applications in nuclear physics, an SRG generator with the kinetic energy
operator is used. With this choice, a fast convergence of many-body
calculations can be achieved, but at the same time substantial three-body
interactions are induced even if one starts from a purely two-nucleon (NN)
Hamiltonian. Three-nucleon (3N) interactions can be handled by modern many-body
methods. However, it has been observed that when including initial chiral 3N
forces in the Hamiltonian, the SRG transformations induce a non-negligible
four-nucleon interaction that cannot be currently included in the calculations
for technical reasons. Consequently, it is essential to investigate alternative
SRG generators that might suppress the induction of many-body forces while at
the same time might preserve the good convergence. In this work we test two
alternative generators with operators of block structure in the harmonic
oscillator basis. In the no-core shell model calculations for 3H, 4He and 6Li
with chiral NN force, we demonstrate that their performances appear quite
promising.
