  In the past few years in-medium similarity renormalization group methods have
been introduced and developed. In these methods the Hamiltonian is evolved
using a unitary transformation in order to decouple a reference state from the
rest of the Hilbert space. The evolution by itself will generate, even if we
start from a two-body interaction, many-body forces which are usually
neglected. In this work we estimate the effect of these residual many-body
forces by comparing results obtained with the Hybrid Multi-determinant method,
which keeps the Hamiltonian within the two-body sector, with the corresponding
ones obtained with the in-medium similarity renormalization group. Although
percentage-wise the effect of neglecting these induced many-body forces is not
too large, they can be appreciable depending on the nucleus, the shell model
space and the harmonic oscillator frequency.
