Recently, Prof. Lu Meng from the School of Physics at Southeast University, in collaboration with Prof. Shi-Lin Zhu’s group at Peking University, developed DeepQuark—the first neural network quantum Monte Carlo framework designed specifically for studying multiquark bound states. Their findings, titled "DeepQuark: A Deep-Neural-Network Approach to Multiquark Bound States," were published in the prestigious physics journal, Physical Review Letters.
Exploring the structure of strongly interacting matter is a cornerstone of modern high-energy nuclear and particle physics. Since 2003, high-energy accelerator experiments worldwide have reported a series of candidates for multiquark states. These states transcend the traditional hadron picture (consisting of a quark-antiquark pair or three quarks) and are likely composed of four or five quarks.
Studying the energy spectra and internal structures of these states is crucial for understanding Quantum Chromodynamics (QCD), the fundamental theory of strong interactions. However, due to the low-energy non-perturbative nature of QCD, the complex interaction mechanisms within multiquark states remain elusive. Furthermore, as quantum many-body systems dominated by strong interactions, multiquark states present significant hurdles for dynamical calculations.
To address these challenges, Lu Meng and his collaborators constructed DeepQuark, the first neural network wavefunction framework for multiquark bound states. The framework leverages the superior ability of neural networks to represent high-dimensional functions. By using physical basis vectors containing symmetry information as input, the team built a wavefunction ansatz that satisfies physical symmetry constraints and accurately describes various multiquark configurations and strong correlation effects. By iteratively training the neural network wavefunction using the variational principle and Monte Carlo algorithms, the framework efficiently solves the Hamiltonian of multiquark systems, yielding high-precision ground-state wavefunctions and energy spectra.
The research team applied the DeepQuark framework to baryons, tetraquarks, and pentaquarks:
· Baryons: The framework efficiently handled both two-body linear confinement potentials and few-body flux-tube-type confinement potentials at nearly identical computational costs, demonstrating its versatility in handling complex interaction potentials.
· Tetraquarks: DeepQuark produced results consistent with traditional numerical methods for highly discussed doubly-heavy and fully-heavy tetraquark systems. It provided a unified description of the mesonic molecule state Tcc and the compact tetraquark state Tbb.
· Pentaquarks: In systems where traditional methods struggle with full dynamical solutions, DeepQuark showed a clear advantage. It successfully performed full quantum calculations of ground-state wavefunctions and predicted a triple-heavy pentaquark bound state corresponding to the Tcc tetraquark.
This study provides a powerful and efficient algorithm for solving complex multiquark systems and exploring the mechanisms of color confinement. It also expands the application of machine learning within high-energy physics and quantum many-body physics.
Wei-Lin Wu, a doctoral student at Peking University, is the lead author of the paper. Prof. Shi-Lin Zhu of Peking University and Prof. Lu Meng of Southeast University serve as the corresponding authors. The work was supported by the National Natural Science Foundation of China, start-up funds for new faculty at Southeast University, the Center for High Energy Physics at Peking University, and the German Research Foundation (DFG).
Link: https://link.aps.org/doi/10.1103/PhysRevLett.132.111901
