发表机构
Centre for Quantum Technologies, National University of Singapore; Department of Materials Science and Engineering, National University of Singapore; INPHYNI, Université Côte d’Azur, CNRS; Department of Physics, Washington University in St. Louis（新加坡国立大学量子技术中心; 新加坡国立大学材料科学与工程系; 尼斯蔚蓝海岸大学CNRS INPHYNI研究所; 圣路易斯华盛顿大学物理系）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文通过本征态到哈密顿量的构造方法，在二维量子自旋系统中系统设计非遍历动力学，揭示了相互作用几何对希尔伯特空间结构及遍历性破缺的控制作用。
AI 中文摘要
非遍历的量子多体动力学为远离平衡态的持续量子相干性提供了一条途径，超越了热化统计力学的传统预期。大多数已知的例子是通过直觉、类比或数值搜索发现的，而非通过系统的哈密顿量设计。这导致在无无序的相互作用量子多体系统中，缺乏通用的方法来工程化稳健的非遍历动力学，尤其是在更高维度中，增强的连通性通常不利于遍历性破缺。在这里，我们使用一种本征态到哈密顿量的构造方法，系统地设计具有可调非遍历性质的二维量子自旋哈密顿量。从一个共同的母模型和输入本征态出发，我们在方格子上构造了两个目标哈密顿量，它们的相互作用几何不同：轴向与对角。我们展示了由此产生的相互作用几何和耦合模式控制着希尔伯特空间结构和动力学。轴向模型形成一个连通的希尔伯特空间网络，并通过抑制共振表现出从遍历到非遍历行为的各向异性驱动的交叉。相比之下，对角模型表现出希尔伯特空间碎裂，并且在其最大的不可约扇区内，显示出量子多体疤痕动力学的特征，包括高度局域化、低纠缠本征态的塔状结构，以及长寿命的相干恢复。这些结果建立了哈密顿量设计、希尔伯特空间网络结构和涌现的非遍历动力学之间的直接联系。
英文摘要
Non-ergodic quantum many-body dynamics offers a route to persistent quantum coherence far from equilibrium, beyond the conventional expectations of thermalizing statistical mechanics. Most known examples have been identified through intuition, analogy, or numerical search, rather than by systematic Hamiltonian design. This leaves few general methods for engineering robust non-ergodic dynamics in disorder-free interacting quantum many-body systems, especially in higher dimensions where enhanced connectivity generally disfavors ergodicity breaking. Here, we use an eigenstate-to-Hamiltonian construction approach to systematically engineer two-dimensional quantum spin Hamiltonians with tunable non-ergodic properties. Starting from a common parent model and input eigenstate, we construct two target Hamiltonians on the square lattice that differ in their interaction geometry: axial versus diagonal. We show that the resulting interaction geometry and coupling pattern control the Hilbert-space structure and dynamics. The axial model forms a connected Hilbert-space network and exhibits an anisotropy-driven crossover from ergodic to non-ergodic behavior through the suppression of resonances. In contrast, the diagonal model exhibits Hilbert-space fragmentation and, within its largest irreducible sector, signatures of quantum many-body scar dynamics including towers of highly localized, low-entanglement eigenstates, and long-lived coherent revivals. These results establish a direct link between Hamiltonian design, Hilbert-space network structure, and emergent non-ergodic dynamics.
Comments19 pages, 12 figures
