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arXiv:2508.03575 · Physics Letters B

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

Zixiao Zhang, Yilong Yang, W. He, Peng-Wei Zhao, Bing-Nan Lu, Y. G.

Published Feb 22, 2026• 2 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1016/j.physletb.2026.140285

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We present the first variational Monte Carlo study of nuclear and hypernuclear excited states within the neural-network quantum states (NQS) framework. We implement both the overlap penalty (OP) and natural excited state (NES) methods to compute low-lying excitation spectra. To address the spin contamination in hypernuclear calculations, we propose a quantum number targeting (QNT) technique for the OP method. Both the OP-QNT and NES methods can reproduce diagonal observables, such as energies and spatial structures, in excellent agreement with rigorous benchmarks. We further provide, to our knowledge, the first ab initio calculation of the M 1 transition strength for Λ 4 H . The calculated transition strength is consistent with the weak-coupling limit, exhibiting a ∼ 1.3% suppression. This work demonstrates that NQS can be elevated from ground-state solvers to practical tools for nuclear and hypernuclear spectroscopy.
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We compute ground-state energies and charge radii of light- to medium-mass nuclei with up to A=58A=58A=58 nucleons, leveraging a variational Monte Carlo method based on Pfaffian-Jastrow neural quantum states. To further understand which elements of the nuclear Hamiltonian are "essential" to predict binding energies and charge radii across the nuclear chart with few-percent errors, we consider different interactions inspired by pionless effective field theory. Specifically, in addition to model "o" of [Phys. Rev. C 103, 054003 (2021)], we study the impact of charge-symmetry-breaking and charge-dependent terms in the nucleon-nucleon force, as well as ppp-wave contributions, which have been found to be critical for the stability of ppp-shell nuclei. In addition to its intrinsic interest, our work assesses the performance of neural quantum states in the medium-mass regime and examines the impact of these interaction modifications. Using the resulting ground-state simulations, we analyze the computational scaling of variational Monte Carlo with neural quantum states as a function of system size and computational resources, enabling projections for future large-scale calculations.
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To distill the essential elements of nuclear binding, we seek the simplest Hamiltonian capable of modeling atomic nuclei with percent-level accuracy. A critical aspect of this endeavor consists of accurately solving the quantum many-body problem without incurring an exponential computing cost with the number of nucleons. We address this challenge by leveraging a variational Monte Carlo method based on a highly expressive neural-network quantum state ansatz. In addition to computing binding energies and charge radii of nuclei with up to A=20 nucleons, by evaluating their magnetic moments, we demonstrate that neural-network quantum states are able to correctly capture the self-emerging nuclear shell structure. To this end, we introduce a novel computational protocol based on adding an external magnetic field to the nuclear Hamiltonian, which allows the neural network to learn the preferred polarization of the nucleus within the given magnetic field.
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