Neural-network-supported basis optimizer for the configuration interaction problem in quantum many-body clusters: Feasibility study and numerical proof

A neural-network approach to optimize the selection of Slater determinants in configuration interaction calculations for condensed-matter quantum many-body systems is developed. We exemplify our algorithm on the discrete version of the single-impurity Anderson model with up to 299 bath sites. Employing a neural network classifier and active learning, our algorithm enhances computational efficiency by iteratively identifying the most relevant Slater determinants for the ground state wave function. We benchmark our results against established methods and investigate the efficiency of our approach compared to another basis truncation scheme without a neural network. Our algorithm demonstrates a substantial improvement in the efficiency of determinant selection, yielding a more compact and computationally manageable basis without compromising accuracy. Given the straightforward application of our neural-network-supported selection scheme to other model Hamiltonians of quantum many-body clusters, our algorithm can significantly advance selective configuration interaction calculations in the context of correlated condensed matter.