多体遍历性 onset 的几何特征
Geometric signatures of the onset of many-body ergodicity
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中文总结 AI 辅助
本研究提出希尔伯特-基林度量，探测多体量子系统遍历区与可积区的边界，该边界由随系统尺寸始终最快增长的特征确定，结论经 Ising 和 PXP 模型数值研究证实。
中文摘要 AI 辅助
识别遍历性 onset 的普适、鲁棒且可解释的特征仍是重大挑战。绝热规范势被指出可作为量子混沌的灵敏探针。本研究将绝热规范势的特征推广至多参数微扰，得到涌现的量子几何，我们将该几何命名为希尔伯特-基林度量，用于研究多体量子系统中遍历性的 onset。我们的希尔伯特-基林度量在所有研究的几何分量上均能灵敏探测遍历区与可积区的边界，该边界由随系统尺寸始终最快增长的存在性唯一确定，这一结论通过对 Ising 模型和 PXP 模型的大量数值研究得到证实。
英文摘要
Identifying universal, robust, and interpretable signatures of the onset of ergodicity remains a major challenge. The adiabatic gauge potential has been noted to act as a sensitive probe of quantum chaos. In this work, we generalize the features of the adiabatic gauge potential to multi-parameter perturbations, yielding an emergent quantum geometry. We dub this geometry the Hilbert-Killing metric, which allows us to study the onset of ergodicity in many-body quantum systems. Our Hilbert-Killing metric sensitively probes the boundary between ergodic and integrable regimes across all investigated geometric components. This boundary is uniquely identified by the presence of the consistently fastest growth with system size, which is corroborated by extensive numerical investigations of the Ising and PXP models.
