Effect of residual many-body forces due to evolution in the in-medium similarity renormalization group method

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. Even if we start from a two-body interaction, the evolution by itself will generate 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 results 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.