AI 中文总结
本研究针对双味伴随矩阵QC₂D模型，探究中间至强耦合区域的低能态性质，发现手征化学势为0时基态的SU(2)_R对称性始终保留，非零时存在量子相变，仅特定参数下该对称性会自发破缺。
AI 中文摘要
在双味伴随矩阵QC₂D的矩阵模型中，我们研究了中间到强（杨-米尔斯）耦合区域的低能态及其性质。该模型具有经典的SU(2)_R手征对称性，哈密顿量的本征态可按其不可约表示（irrep）进行分类。我们利用变分技术构造了在手征化学势c存在时的能量本征态。我们发现，当c=0时，无论耦合强度g如何，基态始终为SU(2)_R单态；然而，当g从中间耦合调至强耦合时，系统会经历从唯一基态到双重简并基态的交叉。强耦合区域的简并性会自发打破轴向ℤ₈对称性，但保留手征对称性。当c≠0时，我们发现存在对应量子相变（QPT）的能级交叉；根据基态的不同，存在三种可能的相，其中仅有一种相的SU(2)_R对称性会自发破缺，且该相仅在g为中间值、c为中等值时出现，在g-c平面中对应一个狭窄窗口，窗口外SU(2)_R对称性始终保留。
英文摘要
In the matrix model of two-flavor adjoint QC$_2$D, we study the low-lying states and their properties in the intermediate-to-strong (Yang-Mills) coupling regime. The model has a classical $SU(2)_R$ chiral symmetry and the eigenstates of the Hamiltonian can be organized in its irreps. We construct the energy eigenstates in presence of a chiral chemical potential $c$ using the variational techniques. We find that when $c=0$, the ground state is always a $SU(2)_R$ singlet, irrespective of the coupling strength $g$. However, as $g$ is tuned from intermediate to strong coupling, the system under goes a crossover from a unique to a doubly degenerate ground state. The degeneracy in the strong coupling regime spontaneously breaks the axial $\mathbb{Z}_8$, while preserving the chiral symmetry. When $c \neq 0$, we find that there can be level crossings which correspond to quantum phase transitions (QPTs). Depending on the ground state, there are three possible phases. The $SU(2)_R$ symmetry is spontaneously broken in only one of these phases, and this phase can only emerge for intermediate $g$ with moderate values of $c$. In the $g-c$ plane this phase corresponds to a narrow window, outside which $SU(2)_R$ is always preserved.
Comments16 pages, 10 figures
