Constructing approximate shell-model wavefunctions by eigenvector continuation

Abstract

Shell-model calculations play a key role in elucidating various properties of nuclei. In general, these 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). This 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 EC, the eigenvectors obtained during the parameter optimization are not necessarily discarded, even if their eigenvalues are far from the experimental data. Those eigenvectors can become accumulated knowledge.