Recursive approach to determine correlation functions in multibaryon systems

Abstract

We propose a recursive algorithm for the calculation of multibaryon correlation functions that combines the advantages of a recursive approach with those of the recently proposed unified contraction algorithm. The independent components of the correlators are built recursively by adding the baryons one after the other in a given order. The list of nonzero independent components is also constructed in a recursive manner, significantly reducing the resources required for this step. We computed the number of operations required to calculate the correlators up to $^{8}\mathrm{Be}$, and observed a significant speedup compared to other techniques. For the calculation of $^{4}\mathrm{He}$ and $^{8}\mathrm{Be}$ correlation functions in the fully relativistic case $\mathcal{O}({10}^{8})$ operations are required, whereas for nonrelativistic operators this number can be reduced to, e.g., $\mathcal{O}({10}^{4})$ in the case of $^{4}\mathrm{He}$.