无序随机图上的三体、二体与局域化
Trimers, pairs and localisation on disordered random graphs
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中文总结 AI 辅助
本文研究图上成对动力学如何涌现群体交互（三体束缚态），发现无序图上三体比单粒子和二体更易局域化，且其玻璃转变阈值远低于单粒子体系，表明群体交互对异质性更敏感。
中文摘要 AI 辅助
高阶网络将群体交互视为既定事实。我探讨的是当群体交互由图上成对动力学产生时会发生什么，并追踪其经历决定其在宏观尺度上是否重要的转变——安德森局域化。涌现超边是哈密顿量的$k$体束缚态，该哈密顿量的项位于图的顶点和边上，当它的所有$(k-1)$体面均未束缚时即为博罗米恩型，在有限图上通过一个$k$重巧合检测到，该巧合在热力学极限下存活，而$(k-1)$重巧合则消失。稀疏随机图从最简单的成对动力学中产生一个这样的超边：三个可区分粒子，具有在位吸引$U$和跳跃$t$，在任何二体束缚之前结合成三体。阈值在贝特格上获得，对于二体为闭式解，在扩展图具有而晶格缺乏的两个扇区中——凝聚体所见扇区和费米液体所见扇区。在无序图上，涌现超边在稀有深位点上成核，并在其组成部分之前局域化：紧凑三体具有窄带和对位能的三重敏感性，在$1.6t$的无序度下经历安德森转变，而单粒子为$17t$，二体为$4t$；三体的费米液体在$1.5t$至$1.7t$之间的线上方为玻璃态，而相同密度下的单粒子液体需要$15t$至$16t$。该转变是单粒子腔体转变，但使用复合体的跳跃和有效无序度。由成对动力学产生的群体交互对其异质性的脆弱性比产生它的网络高一个数量级。
英文摘要
Higher-order networks take group interactions as given. I ask what happens when a group interaction is made by pairwise dynamics on a graph, and follow it through the transition that decides whether it matters at large scale, Anderson localisation. An emergent hyperedge is a $k$-body bound state of a Hamiltonian whose terms live on the vertices and edges of the graph, Borromean when none of its $(k-1)$-body faces is bound, detected on a finite graph by a $k$-fold coincidence that survives the thermodynamic limit while the $(k-1)$-fold ones vanish. Sparse random graphs produce one from the simplest pairwise dynamics: three distinguishable particles with on-site attraction $U$ and hopping $t$ bind into a trimer before any pair binds. The thresholds are obtained on the Bethe lattice, in closed form for the pair, in both sectors that an expander graph has and a lattice lacks, the one a condensate sees and the one a Fermi liquid sees. On a disordered graph the emergent hyperedges nucleate on rare deep sites and localise before their parts: the compact trimer, with a narrow band and a threefold sensitivity to site energies, undergoes the Anderson transition at a disorder of $1.6t$, against $17t$ for a single particle and $4t$ for a pair, and the Fermi liquid of trimers is a glass above a line between $1.5t$ and $1.7t$, where a liquid of single particles at the same density needs $15t$ to $16t$. The transition is the single-particle cavity transition with the composite's hopping and effective disorder. A group interaction made by pairwise dynamics is an order of magnitude more fragile to heterogeneity than the network that makes it.
发表机构
- Nodes & Links Ltd（Nodes & Links 有限公司）
机构由 AI 辅助整理，请以论文原文为准。
