Constructing approximate shell-model wavefunctions by eigenvector continuation

Abstract

Shell-model calculations play a key role in elucidating various properties of nuclei. In general, those studies require a huge number of calculations to be repeated for parameter calibration and quantifying uncertainties. To reduce the computational burden, we propose a new workflow of shell-model calculations using a method called eigenvector continuation (EC). It enables us to efficiently approximate the eigenpairs under a given Hamiltonian by previously sampled eigenvectors. We demonstrate the validity of EC as an emulator of the valence shell-model, including first application of EC to electromagnetic transition matrix elements. Furthermore, we propose a new usage of EC: preprocessing, in which we start the Lanczos iterations from the approximate eigenvectors, and demonstrate that this can accelerate subsequent research cycles. With the aid of the EC, the eigenvectors obtained during the parameter optimization are not necessarily to be discarded, even if their eigenvalues are far from the experimental data. Those eigenvectors can become accumulated knowledge.