Bose-Hubbard菱形项链晶格中的局域希尔伯特空间碎片化与弱热化
Local Hilbert space fragmentation and weak thermalization in Bose-Hubbard diamond necklaces
AI总结：
通过基矢旋转揭示Bose-Hubbard菱形项链晶格中由紧凑局域态守恒量标识的希尔伯特空间碎片化，发现子扇区限制下的弱热化及从面积律到对数增长的纠缠标度，并解释了穹顶可区分性随中心位点增加而增强的图结构机制。
摘要：
我们研究了一族具有n个中心位点的菱形项链晶格中的Bose-Hubbard模型。这些模型的单粒子谱呈现出紧凑局域态（CLSs），它们占据每个菱形的上和下位点。通过进行适当的基矢旋转，多玻色子希尔伯特空间的碎片化在哈密顿量的邻接图中变得明显，显示出维度范围广泛的互不连通的子扇区。这些模型具有一个与单粒子CLSs占据数相关的守恒量，该守恒量唯一地标识了多玻色子希尔伯特空间的不同子扇区。由于希尔伯特空间的碎片化，系统纠缠熵的分布呈现出嵌套穹顶结构。我们通过子扇区限制的纠缠演化发现了弱热化，并观察到从面积律到对数增长的广泛纠缠熵标度行为。此外，我们观察到不同穹顶之间的可区分性随着中心位点数量的增加而增强，并通过分析哈密顿量的图结构解释了这一现象背后的机制。
英文摘要：
We study Bose-Hubbard models in a family of diamond necklace lattices with $n$ central sites. The single-particle spectrum of these models presents compact localized states (CLSs) that occupy the up and down sites of each diamond. By performing an appropriate basis rotation, the fragmentation of the many-boson Hilbert space becomes apparent in the adjacency graph of the Hamiltonian, showing disconnected sub-sectors with a wide range of dimensions. The models present a conserved quantity related to the occupation of the single-particle CLSs that uniquely identifies the different sub-sectors of the many-boson Hilbert space. Due to the fragmentation of the Hilbert space, the distribution of entanglement entropies of the system presents a nested-dome structure. We find weak thermalization through sub-sector-restricted entanglement evolution and a wide range of entanglement entropy scalings from area-law to logarithmic growth. Additionally, we observe how the distinguishability between the different domes increases with the number of central sites and we explain the mechanism behind this fact by analyzing the graph structure of the Hamiltonian.
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