标题： 耦合三聚体系统在半填充下的相图使用哈伯德模型 显示英文标题

标题： Phase diagram of a coupled trimer system at half filling using the Hubbard model

摘要： 平坦带系统由于在小扰动下的不稳定性而最近引起了广泛关注，这可能导致许多奇特量子相的稳定。 我们研究了一种三聚体梯子，在没有局域库仑相互作用的情况下，它显示出中间平坦带。 我们使用精确对角化（ED）、密度矩阵重正化群（DMRG）和微扰理论研究了该几何结构上的哈伯德模型的量子相。 我们在下一邻近跃迁参数$t_2$和局域库仑相互作用$U$的平面上构建了量子相图，揭示了五个不同的量子相。 在低$U$和中等至高幅度的$t_2$下，系统表现出金属行为，而在大$U$和小幅度的$t_2$下，它会过渡到类似于某些三聚体材料中观察到的铁磁绝缘体相。 在小$t_2$极限下，费米能级位于平坦带中，导致电子在三聚体内的局域化。 在低$U$和小幅度的$t_2$时，平带机制有利于绝缘反铁磁性，而在大$U$时，反铁磁态源于三聚体相邻位点和孤立角自旋之间的单重态二聚体形成，这些位点以铁磁方式连接。 绝缘的晶格自旋密度波相由于竞争的最近邻跃迁，表现出上-上-下-下的自旋排列，$t_1$。 有趣的是，在中等$U$和$|t_2|>0.3$时，基态表现得像金属汤川-卢特利尔液体。 显示英文摘要

摘要： Flat band systems have recently attracted significant attention due to their instability under small perturbations, which can lead to the stabilization of many exotic quantum phases. We study a trimer ladder which shows a middle flat band in the absence of onsite Coulomb interaction. We investigate the quantum phases of the Hubbard model on this geometry using exact diagonalization (ED), density matrix renormalization group (DMRG), and perturbation theory. We construct a quantum phase diagram in the plane of the next-nearest-neighbor hopping parameter $t_2$ and onsite Coulomb interaction $U$, revealing five distinct quantum phases. At low $U$ and moderate to high magnitude of $t_2$, the system exhibits metallic behavior, while at large $U$ and small magnitude of $t_2$, it transitions to a ferrimagnetic insulator phase, similar to those observed in certain trimer materials. In the small $t_2$ limit, the Fermi energy is in the flat band, leading to localization of the electrons within the trimer. At low $U$ and small magnitude of $t_2$, the flat band mechanism favors insulating ferrimagnetism, whereas at large $U$, ferrimagnetic states emerge from singlet dimer formation between neighboring sites of a trimer and an isolated corner spin, which connect ferromagnetically. The insulating cell spin density wave phase displays an up-up-down-down spin configuration due to competing nearest neighbor hopping, $t_1$. Interestingly, in moderate $U$ and $|t_2|>0.3$, the ground state behaves like metallic Tomonaga-Luttinger liquid.