论文标题
一些强烈相互作用的颗粒的能量自组织
Energetical self-organization of a few strongly interacting particles
论文作者
论文摘要
我们研究了一些与强距离相互作用的一些相互作用粒子的量子自组织。物理系统是通过2D哈伯德方格晶格模型建模的，其强度u的邻接术语最近，第二个邻居的跳跃t。对于t = 0，系统的能量取决于哈伯德晶格中相邻位点上的颗粒之间的键数。我们发现，在系统的不同填充物处，该键顺序一直存在于地面和系统的某些激发态，以实现强烈的相互作用强度。在我们的分析中，我们使用由真实空间（Fock状态）中粒子形成的网络/图网格结构的Euler特征，这有助于量化能量（键）排序。我们发现多个地面和激发态，具有整数Euler号码，其值始于$ t = 0 $ case，用于强互动$ u >> t $。基态的相应量子相包含低填充物的密度波 - 波（DWO），其中颗粒彼此分开形成，或用于高填充物的聚类订单（CO），其中粒子在凝结成簇中时形成各种结构。此外，我们发现了包含Fock状态叠加的各种激发态，其概率幅度是自调的，其方式可以从$ t = 0 $限制中保留Euler特性的整数值。
We study the quantum self-organization of a few interacting particles with strong short-range interactions. The physical system is modeled via a 2D Hubbard square lattice model, with a nearest-neighbor interaction term of strength U and a second nearest-neighbor hopping t. For t=0 the energy of the system is determined by the number of bonds between particles that lie on adjacent sites in the Hubbard lattice. We find that this bond order persists for the ground and some of the excited states of the system, for strong interaction strength, at different fillings of the system. For our analysis we use the Euler characteristic of the network/graph grid structures formed by the particles in real space (Fock states), which helps to quantify the energetical(bond) ordering. We find multiple ground and excited states, with integer Euler numbers, whose values persist from the $t=0$ case, for strong interaction $U>>t$. The corresponding quantum phases for the ground state contain either density-wave-order(DWO) for low fillings, where the particles stay apart form each other, or clustering-order(CO) for high fillings, where the particles form various structures as they condense into clusters. In addition, we find various excited states containing superpositions of Fock states, whose probability amplitudes are self-tuned in a way that preserves the integer value of the Euler characteristic from the $t=0$ limit.
