标题： 棋盘格晶格上的$\mathrm{SU}\left(3\right)$自旋模型的基态 显示英文标题

标题： Ground State of $\mathrm{SU}\left(3\right)$ spin model on the checkerboard lattice

摘要： 量子自旋系统中的几何阻挫可能导致奇特的基态。 在本研究中，我们研究棋盘格晶格上的$\mathrm{SU}(3)$自旋模型，以探索其点连接的$(N+1)$站点局部结构引起的阻挫效应。 我们采用密度矩阵重正化群（DMRG）和精确对角化（ED）技术来确定基态特性。 我们的结果揭示了既没有三子晶格反铁磁序也没有价键簇固态序。 相反，我们识别出对边界条件和系统大小敏感的具有键条纹图案的基态，包括交错单态阵列和均匀平坦条纹。 值得注意的是，这些条纹相对解耦，类似的图案可以在准一维梯子中重建。 这些发现表明，几何阻挫使系统趋向于一种混合相，结合了自旋液体和价键簇固态的特征，为受阻挫量子自旋系统的行为提供了新的见解。 显示英文摘要

摘要： Geometric frustration in quantum spin systems can lead to exotic ground states. In this study, we investigate the $\mathrm{SU}(3)$ spin model on the checkerboard lattice to explore the effects of frustration arising from its point-connected $(N+1)$-site local structure. We employ density matrix renormalization group (DMRG) and exact diagonalization (ED) techniques to determine the ground state properties. Our results reveal the absence of both 3-sublattice antiferromagnetic order and valence cluster solid order. Instead, we identify ground states with bond stripe patterns sensitive to boundary conditions and system size, comprising staggered singlet arrays and uniform flat stripes. Notably, these stripes are relatively decoupled, and similar patterns can be reconstructed in quasi-one-dimensional ladders. These findings suggest that geometric frustration drives the system toward a mixed phase, combining characteristics of spin-liquid and valence cluster solid states, providing new insights into the behavior of frustrated quantum spin systems.