通过态图几何与态图异质性识别多体量子系统中的慢弛豫
Identifying slow relaxation in many-body quantum systems through state-graph geometry and state-graph heterogeneity
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中文总结 AI 辅助
该研究借助量子随机游走理论，通过多体态图几何与异质性，分析三个典型多体量子模型的慢弛豫动力学，发现击中矩阵谱半径可作为高灵敏相变指标，为慢弛豫相提供几何表征框架。
中文摘要 AI 辅助
我们采用量子随机游走理论的工具，借助多体态图研究慢弛豫动力学。具体而言，我们利用幺正时间演化算子导出的击中时间，构建了基态之间异质性的探测方法。我们发现，由基态间成对击中时间编码的态图几何，是多种系统中慢弛豫动力学的高灵敏指标。我们研究了三个典型模型：Rosenzweig-Porter模型、量子East模型和三角晶格气体模型，这些模型在调控某个控制参数时会出现慢动力学的突发起始。作为图几何的全局表征，我们分析了击中矩阵的谱半径，发现其在慢动力学起始时急剧增大，跨越多个数量级，在相变处存在特征交叉点。我们的工作为使用统一的图论形式化方法描述和识别具有慢弛豫的相提供了几何框架。
英文摘要
We adapt tools from the theory of quantum random walks to investigate slow relaxation dynamics through the many-body state graph. Specifically, we construct a probe of heterogeneity between basis states defined using hitting times derived from the unitary time-evolution operator. We find that the state-graph geometry, encoded by the pairwise hitting time of basis states, is a highly sensitive indicator of slow relaxation dynamics in a variety of systems. We study three paradigmatic models: the Rosenzweig-Porter model, the quantum East model, and the triangular lattice gas model, exhibiting a sudden onset of slow dynamics upon tuning of a control parameter. As a global characterization of the graph geometry, we analyze the spectral radius of the hitting matrix. We find that it increases sharply at the onset of slow dynamics, spanning many orders of magnitude, with a characteristic crossing point at the transition. Our work provides a geometric framework for describing and identifying phases with slow relaxation using a unified graph-theoretic formalism.
