论文标题
重新归一化的方法来分析和设计赫尔米尔人和非富尔米特界面
Renormalization approach to the analysis and design of Hermitian and non-Hermitian interfaces
论文作者
论文摘要
我描述了一种具体而有效的真实空间重新归一化方法，该方法在广泛的Hermitian和非热模型中为界面状态提供了统一的观点，而不论它们是否遵守传统的散装原则。新兴界面物理受微观界面参数的流动，界面状态的属性与该流量的固定点拓扑链接在一起。特别是，接口状态的量化条件将收敛性问题相同转换为不稳定的固定点。作为其关键优点，该方法可以直接应用于混凝土模型，并用于设计具有所需特性的状态的界面，例如具有预定且可能破坏对称性的状态。我通常开发方法，然后在各种设置中演示这些特征，包括用于设计二维系统边缘的圆形，三角形和方形的复杂分散带和相关弧。此外，我描述了这种方法如何转移到非线性设置，并通过分布式饱和的增益和损失来证明此扩展的效率，实用性和一致性。
I describe a concrete and efficient real-space renormalization approach that provides a unifying perspective on interface states in a wide class of Hermitian and non-Hermitian models, irrespective of whether they obey a traditional bulk-boundary principle or not. The emerging interface physics are governed by a flow of microscopic interface parameters, and the properties of interface states become linked to the fixed-point topology of this flow. In particular, the quantization condition of interface states converts identically into the question of the convergence to unstable fixed points. As its key merit, the approach can be directly applied to concrete models and utilized to design interfaces that induce states with desired properties, such as states with a predetermined and possibly symmetry-breaking energy. I develop the approach in general, and then demonstrate these features in various settings, including for the design of circular, triangular and square-shaped complex dispersion bands and associated arcs at the edge of a two-dimensional system. Furthermore, I describe how this approach transfers to nonlinear settings, and demonstrate the efficiency, practicability and consistency of this extension for a paradigmatic model of topological mode selection by distributed saturable gain and loss.
