Automating IMSRG(3) expression generation with Python

The IMSRG (in-medium similarity renormalization group) is a powerful theoretical method for studying medium-mass nuclei. However, manually deriving the expressions needed for IMSRG calculations is time-consuming and error-prone. In this work, we develop a fully automated Python framework to generate and evaluate IMSRG expressions. We benchmark our code against the existing IMSRG codebase with promising accuracy. This project allows for the future exploration of new nested commutator structures, which we will use to improve the accuracy of existing nuclear calculations.

A more in-depth background and motivation: The standard IMSRG framework is IMSRG(2), which only includes the nested commutators that involve two-body operators or less at every intermediate step. This leaves out many three-body terms (e.g., [2,2]3, [2,[2,3]3]2) from its calculations, causing inaccuracies. The IMSRG(3) framework includes all the missing three-body terms, but many of these terms are not only computationally expensive but have little impact on the final result. We want to explore which higher-body commutators are worth computing, but it is infeasible to do this manually. The triple-nested commutators that we are interested in come with hundreds of diagrams, which all would require separate routines to write by hand. Our automated code uses only one general routine for all diagrams, allowing us to explore these diagrams significantly faster.