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Fully heavy multiquarks in neural-network quantum states

Wen-min Li1,2,3, Zhenyu Zhang1,2,3,4,5,†, and Qian Wang1,3,6,*

  • *Contact author: qianwang@m.scnu.edu.cn
  • †These author contributed equally to this work.
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Phys. Rev. D 114, 074033 – Published 13 October, 2026

DOI: https://doi.org/10.1103/v5ld-7t21

Abstract

Exotic hadrons beyond the conventional quark model provide a direct window into the dynamics of strong interaction. However, extracting the multiquark spectroscopy has to face the quantum many-body problem, which is still a theoretical challenge. In this case, diquark-antidiquark model is proposed as an approximation. Although this model can describe the spectroscopy roughly, it cannot describe the detailed dynamics. Furthermore, the methods aiming at dealing with many-body problem, e.g., the Gaussian expansion method and diffusion Monte Carlo, are proposed, but face severe computational bottlenecks. In this work, we introduce the neural-network quantum state (NNQS) approach to investigate the spectra of fully heavy multiquark states within the nonrelativistic potential quark model. By employing deep neural networks to represent the complex many-body spatial wave function, and constructing the color-spin part exactly from group theory to enforce fermionic antisymmetry, our approach effectively overcomes the dimensionality obstacles inherent in traditional methods. The results are compared with various model calculations, demonstrating that NNQS offers superior accuracy and flexibility, particularly in treating high-dimensional correlations. This work establishes NNQS as a promising tool for exploring the spectroscopy of exotic hadrons.

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Phys. Rev. D 114, 074033– Published 13 October, 2026
  • Received 30 August 2026
  • Accepted 24 September 2026
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