Factorized Approximation to the IMSRG(3)

We describe an approximation to the in-medium similarity renormalization group (IMSRG) method in which we include the effects of intermediate three-body operators arising within nested commutators. As an initial step, we present the relevant equations for two nested commutators, all of which can be factorized so that the method scales like the standard IMSRG(2) approximation, enabling large-scale calculations. We test the accuracy of this approximation scheme, and apply it to the isotopic chains of carbon, sulfur and nickel isotopic chains. We obtain an improved description of spectroscopy, and a reduced dependence on the choice of the valence space. In addition, we provide an explanation of the relative importance of the diagram topologies included, with an eye toward assessing the impact of remaining omitted terms.