Using variational methods, we numerically investigate the matrix model for the two-color QCD coupled to a single quark (${\text{matrix-QCD}}_{2,1}$) in the limit of ultrastrong Yang-Mills coupling ($g=\infty$). The spectrum of the model has superselection sectors labeled by baryon number $B$ and spin $J$. We study sectors with $B=0$, 1, 2 and $J=0$, 1, which may be organized as mesons, (anti-)diquarks and (anti-)tetraquarks. For each of these sectors, we study the properties of the respective ground states in both chiral and heavy quark limits, and uncover a rich quantum phase transition (QPT) structure. We also investigate the division of the total spin between the glue and the quark and show that glue contribution is significant for several of these sectors. For the $(B,J)=(0,0)$ sector, we find that the dominant glue contribution to the ground state comes from reducible connections. Finally, in the presence of nontrivial baryon chemical potential $\mu$, we construct the phase diagram of the model. For sufficiently large $\mu$, we find that the ground state of the theory may have nonzero spin.

中文翻译：

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二色一味QCD矩阵模型：超强耦合机制


使用变分方法，我们数值研究了耦合到单夸克的双色 QCD 的矩阵模型（ ${\text{matrix-QCD}}_{2,1}$ ）在超强杨-米尔斯耦合的极限（ $g=\infty$ ）。该模型的频谱具有由重子数标记的超选择扇区 $B$ 并旋转 $J$ 。我们研究行业 $B=0$ 、 1、 2 和 $J=0$ ，1，可以组织为介子、（反）二夸克和（反）四夸克。对于每个部分，我们研究了手性夸克极限和重夸克极限下各自基态的性质，并揭示了丰富的量子相变（QPT）结构。我们还研究了胶和夸克之间总自旋的划分，并表​​明胶的贡献对于其中几个部分是重要的。对于 $(B,J)=(0,0)$ 部门中，我们发现对基态的主要胶贡献来自于可还原的连接。最后，在存在非平凡重子化学势的情况下 $\mu$ ，我们构建模型的相图。对于足够大的 $\mu$ ，我们发现理论的基态可能具有非零自旋。