Machine learning the single-Λ hypernuclei with neural-network quantum states

A thorough description of baryonic system beyond first-generation quark sector is indispensable for the maturation of nuclear ab initio methods. This study pioneers the application of neural-network quantum states to hypernuclei, with trainable parameters determined by variational Monte Carlo approach (VMC-NQS). In order to reduce the numerical uncertainty and treat the nucleons and hyperons in a unified manner, spinor grouping (SG) method is proposed to analytically integrate out isospin degrees of freedom. With SG method and spin symmetry enforcement, the Λ separation energies of s -shell hypernuclei are computed with one-thousandth level accuracy and benchmarked against existing results from stochastic variational method, showing superior performance. By comparing two different sets of Hamiltonian based on pionless effective field theory ( π ̸ EFT), we choose an optimal model and further carry out calculations of selected p -shell charge-symmetric hypernuclei with mass number up to 13, exhibiting satisfactory consistency with experimental results. Our work underscores the potential of the VMC-NQS family for the in-depth probing of hypernuclear systems.