AI 中文总结
研究在任意图面上构造精确平坦能带哈密顿量的方法，利用阿蒂亚 - 辛格指标定理离散图推广证明简并性受局部拓扑保护，产生紧致局域态，探讨其在量子网络、机器学习及拓扑量子计算等方面的意义。
AI 中文摘要
强关联量子物质本质上由非对易量子算符之间的张力定义。具有宏观简并性的哈密顿量在该领域备受关注，因其对任何非对易微扰都有无限敏感性。在莫尔异质结构中，通过在动能哈密顿量中设计这种广泛简并性，可为从所得平坦能带中涌现出奇异强关联物质相创造条件。本文介绍一种在任意图的面上构造无穷多个精确平坦能带哈密顿量的方法，并在四个布拉伐格子的面上进行了演示。利用阿蒂亚 - 辛格指标定理的离散图推广，证明了此类面图哈密顿量的广泛简并性受面图连通性的局部拓扑保护。由此产生的宏观零空间产生紧致局域态，由于跳跃路径的受挫，这些态随时间保持局域化。我们讨论了这种非色散量子模式在多种场景中的广泛意义，从量子网络和量子机器学习算法中的停滞动力学到无马约拉纳拓扑量子计算。
英文摘要
Strongly correlated quantum matter is fundamentally defined by the tension between non-commuting quantum operators. Hamiltonians exhibiting macroscopic degeneracies are of general interest in this field because they imply an infinite susceptibility to any non-commuting perturbation. In moiré heterostructures, engineering such extensive degeneracies in the kinetic Hamiltonian creates a fertile garden for exotic strongly correlated phases of matter to emerge from the resulting flat bands. Here, we introduce a prescription to construct an infinite family of exact flat band Hamiltonians supported on the faces of arbitrary graphs. We demonstrate this algorithm on the faces of four Bravais lattices. Using a discrete graph generalization of the Atiyah-Singer index theorem, we prove that the extensive degeneracies of such face-graph Hamiltonians are protected by the local topology of the face-graph connectivity. The resulting macroscopic null spaces yield compact localised states that remain localised over time due to frustration in hopping pathways. We discuss the broad implications of such non-dispersing quantum modes in diverse settings, from arrested dynamics in quantum networks and quantum machine learning algorithms to Majorana-free topological quantum computation.
Comments19 pages main text, 8 figures, 1 appendix. Comments welcome and will be gratefully acknowledged upon submission
