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

## TL;DR

This paper investigates the impact of residual many-body forces generated during the in-medium similarity renormalization group evolution, comparing results with and without these forces to assess their significance in nuclear structure calculations.

## Contribution

It provides an estimation of the effects of residual many-body forces in IMSRG calculations by comparing with the Hybrid Multi-determinant method, highlighting their potential importance.

## Key findings

- Residual many-body forces can have appreciable effects depending on nucleus and model parameters.
- Neglecting these forces may lead to inaccuracies in nuclear structure predictions.
- The effect size varies but is generally not negligible.

## Abstract

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.