Machine learning the single-$\Lambda$ hypernuclei with neural-network quantum states

TL;DR

This paper introduces neural-network quantum states combined with variational Monte Carlo to accurately model single-$\Lambda$ hypernuclei, demonstrating superior performance and potential for understanding hypernuclear interactions.

Contribution

It pioneers the use of neural-network quantum states for hypernuclei, proposing spinor grouping and spin purification methods to improve accuracy and treat nucleons and hyperons uniformly.

Findings

Achieved one-thousandth level accuracy in $s$-shell hypernuclei energy spectra.

Benchmarked results against stochastic variational methods showing superior performance.

Validated the effectiveness of pionless EFT in modeling hypernuclei up to mass number 13.

Abstract

Single-$\Lambda$ hypernuclei are the most straightforward extension of atomic nuclei. 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. A novel spin purification scheme is developed to address the severe spin contamination occurring in standard energy minimization due to the weakly bound characteristic of light single-$\Lambda$ hypernuclei. The energy spectrum of $s$-shell hypernuclei is computed with one-thousandth level accuracy and benchmarked against existing stochastic variational results, showing superior performance. By comparing two different sets of Hamiltonian based on pionless effective field theory (pionless 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 findings underscore the potential of VMC-NQS family in approaching exact solution of few-body systems and the accuracy of pionless EFT in modeling hypernuclei. This is crucial for understanding hyperon-nucleon-nucleon and hyperon-hyperon-nucleon interactions, providing a powerful tool for precisely predicting the properties of multi-strangeness hypernuclei.