双曲能带理论中的量子几何
Quantum Geometry in Hyperbolic Band Theory
浏览论文内容
中文总结 AI 辅助
本研究提出全息抖动技术，在双曲能带理论中动态提取量子度量，并在{8,3}和类kagome晶格上验证，为探测双曲量子几何和拓扑现象奠定基础。
中文摘要 AI 辅助
双曲能带理论（HBT）最近在负曲率空间中揭示了许多奇异的物理现象。与此同时，量子度量已作为控制量子几何和拓扑相的基本张量而出现。在本快报中，我们通过研究HBT中的量子度量来连接这两个前沿领域。由于传统的欧几里得度量提取协议在这些非交换几何中根本失效，我们引入了全息抖动（holonomy shaking），这是一种新颖的、实验上可行的技术，利用周期性晶格驱动来动态提取度量。以{8,3}正则双曲晶格和类kagome晶格为具体例子，我们展示了量子度量的高保真度动态提取。我们的结果为探测双曲量子几何建立了稳健的蓝图，为在双曲量子物质中发现奇异拓扑现象铺平了道路。
英文摘要
Hyperbolic band theory (HBT) has recently unveiled a wealth of exotic physical phenomena in negatively curved spaces. Concurrently, the quantum metric has emerged as a fundamental tensor governing quantum geometry and topological phases. In this Letter, we bridge these two frontiers by investigating the quantum metric in HBT. Because conventional Euclidean metric extraction protocols fundamentally fail in these non-commutative geometries, we introduce holonomy shaking, a novel, experimentally viable technique utilizing periodic lattice driving to dynamically extract the metric. Using the {8,3} regular hyperbolic and kagome-like lattices as concrete examples, we demonstrate the high-fidelity dynamical extraction of the quantum metric. Our results establish a robust blueprint for probing hyperbolic quantum geometries, paving the way for the discovery of exotic topological phenomena in hyperbolic quantum matter.
发表机构
- University of Saskatchewan（萨斯喀彻温大学）
- Julius-Maximilians-Universität Würzburg（维尔茨堡朱利叶斯-马克西米利安大学）
机构由 AI 辅助整理，请以论文原文为准。
