拓扑平带中的 Thouless 量子行走
Thouless quantum walks in topological flat bands
AI总结：
本文提出利用非阿贝尔 Thouless 泵浦在简并拓扑平带中构造一维离散时间量子行走，通过完整硬币与位移算子编码拓扑几何性质，并揭示类 Weyl 动力学及宇称、时间反演对称性破缺的联系。
摘要：
非阿贝尔规范对称性是现代理论物理的基石，构成了基本相互作用以及量子力学几何结构的基础。然而，它们在工程量子系统中控制量子相干、纠缠和输运的潜力，在很大程度上仍未得到探索。在本工作中，我们提出利用非阿贝尔 Thouless 泵浦，在以简并平带为特征的拓扑晶格上实现一维离散时间量子行走。通过精心设计的泵浦循环，我们实现了不同类别的完整硬币算子与位移算子。该框架允许构建编码底层系统拓扑和几何性质的量子行走。值得注意的是，所得演化表现出宇称对称性破缺，并产生由类 Weyl 方程支配的动力学过程，突显了系统中宇称对称性破缺与时间反演对称性破缺之间的深刻联系。
英文摘要：
Non-Abelian gauge symmetries are cornerstones of modern theoretical physics, underlying fundamental interactions and the geometric structure of quantum mechanics. However, their potential to control quantum coherence, entangle- ment, and transport in engineered quantum systems remains to a large extent unexplored. In this work, we propose utilizing non-Abelian Thouless pumping to realize one-dimensional discrete-time quantum walks on topological lattices char- acterized by degenerate flat bands. Through carefully designed pumping cycles, we implement different classes of holonomic coin and shift operators. This frame- work allows for the construction of quantum walks that encode the topological and geometric properties of the underlying system. Remarkably, the resulting evolution exhibits parity symmetry breaking and gives rise to a dynamical pro- cess governed by a Weyl-like equation, highlighting the deep connection between parity and time-reversal symmetry breaking in the system.
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