Authors: Anonymous | L. Meng | Shi-Lin Zhu
Source: Physical Review Letters (article, 2026-01-28)
Field: Materials Science — Materials Chemistry

DeepQuark: A Deep-Neural-Network Approach to Multiquark Bound States For the first time, we implement the deep-neural-network-based variational Monte Carlo approach for the multiquark bound states, whose complexity surpasses that of electron or nucleon systems due to strong SU(3) color interactions. We design a novel and high-efficiency architecture, DeepQuark, to address the unique challenges in multiquark systems such as stronger correlations, extra discrete quantum numbers, and intractable confinement interaction. Our method demonstrates competitive performance with state-of-the-art approaches, including diffusion Monte Carlo and Gaussian expansion method, in the nucleon, doubly heavy tetraquark, and fully heavy tetraquark systems. Notably, it outperforms existing calculations for pentaquarks, exemplified by the triply heavy pentaquark. For the nucleon, we successfully incorporate three-body flux-tube confinement interactions without additional computational costs. In tetraquark systems, we consistently describe hadronic molecule <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"> <a:mrow> <a:msub> <a:mrow> <a:mi>T</a:mi> </a:mrow> <a:mrow> <a:mi>c</a:mi> <a:mi>c</a:mi> </a:mrow> </a:msub> </a:mrow> </a:math> and compact tetraquark <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"> <c:mrow> <c:msub> <c:mrow> <c:mi>T</c:mi> </c:mrow> <c:mrow> <c:mi>b</c:mi> <c:mi>b</c:mi> </c:mrow> </c:msub> </c:mrow> </c:math> with an unbiased form of wave function ansatz. In the pentaquark sector, we obtain weakly bound <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"> <e:mrow> <e:msup> <e:mrow> <e:mover accent="true"> <e:mrow> <e:mi>D</e:mi> </e:mrow> <e:mrow> <e:mo stretchy="false">¯</e:mo> </e:mrow> </e:mover> </e:mrow> <e:mrow> <e:mo>*</e:mo> </e:mrow> </e:msup> <e:msubsup> <e:mrow> <e:mi mathvariant="normal">Ξ</e:mi> </e:mrow> <e:mrow> <e:mi>c</e:mi> <e:mi>c</e:mi> </e:mrow> <e:mrow> <e:mo>*</e:mo> </e:mrow> </e:msubsup> </e:mrow> </e:math> molecule <j:math xmlns:j="http://www.w3.org/1998/Math/MathML" display="inline"> <j:mrow> <j:msub> <j:mrow> <j:mi>P</j:mi> </j:mrow> <j:mrow> <j:mi>c</j:mi> <j:mi>c</j:mi> <j:mover accent="true"> <j:mrow> <j:mi>c</j:mi> </j:mrow> <j:mrow> <j:mo stretchy="false">¯</j:mo> </j:mrow> </j:mover> </j:mrow> </j:msub> <j:mo stretchy="false">(</j:mo> <j:mn>5715</j:mn> <j:mo stretchy="false">)</j:mo> </j:mrow> </j:math> with <p:math xmlns:p="http://www.w3.org/1998/Math/MathML" display="inline"> <p:mrow> <p:mi>S</p:mi> <p:mo>=</p:mo> <p:mfrac> <p:mrow> <p:mn>5</p:mn> </p:mrow> <p:mrow> <p:mn>2</p:mn> </p:mrow> </p:mfrac> </p:mrow> </p:math> and its bottom partner <r:math xmlns:r="http://www.w3.org/1998/Math/MathML" display="inline"> <r:mrow> <r:msub> <r:mrow> <r:mi>P</r:mi> </r:mrow> <r:mrow> <r:mi>b</r:mi> <r:mi>b</r:mi> <r:mover accent="true"> <r:mrow> <r:mi>b</r:mi> </r:mrow> <r:mrow> <r:mo stretchy="false">¯</r:mo> </r:mrow> </r:mover> </r:mrow> </r:msub> <r:mo stretchy="false">(</r:mo> <r:mn>15569</r:mn> <r:mo stretchy="false">)</r:mo> </r:mrow> </r:math> . They can be viewed as the analogs of the molecular <x:math xmlns:x="http://www.w3.org/1998/Math/MathML" display="inline"> <x:mrow> <x:msub> <x:mrow> <x:mi>T</x:mi> </x:mrow> <x:mrow> <x:mi>c</x:mi> <x:mi>c</x:mi> </x:mrow> </x:msub> </x:mrow> </x:math> . We recommend experimental search of <z:math xmlns:z="http://www.w3.org/1998/Math/MathML" display="inline"> <z:mrow> <z:msub> <z:mrow> <z:mi>P</z:mi> </z:mrow> <z:mrow> <z:mi>c</z:mi> <z:mi>c</z:mi> <z:mover accent="true"> <z:mrow> <z:mi>c</z:mi> </z:mrow> <z:mrow> <z:mo stretchy="false">¯</z:mo> </z:mrow> </z:mover> </z:mrow> </z:msub> <z:mo stretchy="false">(</z:mo> <z:mn>5715</z:mn> <z:mo stretchy="false">)</z:mo> </z:mrow> </z:math> in the D-wave <fb:math xmlns:fb="http://www.w3.org/1998/Math/MathML" display="inline"> <fb:mrow> <fb:mi>J</fb:mi> <fb:mo>/</fb:mo> <fb:mi>ψ</fb:mi> <fb:msub> <fb:mrow> <fb:mi mathvariant="normal">Λ</fb:mi> </fb:mrow> <fb:mrow> <fb:mi>c</fb:mi> </fb:mrow> </fb:msub> </fb:mrow> </fb:math> channel. DeepQuark holds great promise for extension to larger multiquark systems, overcoming the computational barriers in conventional methods. It also serves as a powerful framework for exploring confining mechanism beyond two-body interactions in multiquark states, which may offer valuable insights into nonperturbative QCD and general many-body physics. Tetraquark ; Hadron ; Bound state ; Quantum Monte Carlo ; Pentaquark ; Monte Carlo method ; Gaussian ; Wave function Machine Learning in Materials Science ; Quantum many-body systems ; Quantum Computing Algorithms and Architecture