非均匀SSH链中空间扩展零模的普适标度
Universal scaling of spatially extended zero modes in inhomogeneous SSH chains
AI总结：
研究非均匀SSH模型的平滑拓扑界面，发现其关联的Jackiw-Rebbi零模空间扩展，晶格扩展普适标度为系统尺寸平方根，确立了支配平滑拓扑界面低能物理的普适临界长度。
AI中文摘要：
受保护的零模是物质拓扑相的标志，它们以指数形式局域在不同有隙相之间的陡峭界面处。我们研究了在一大类非均匀Su-Schrieffer-Heeger（SSH）模型中，平滑界面如何改变这一图像。结合精确的晶格解与非均匀狄拉克描述，我们证明相关的Jackiw-Rebbi零模变为空间扩展的。对于任意平滑的跳跃轮廓，其晶格扩展普适地标度为系统尺寸的平方根，与界面的微观细节无关。这一涌现长度定义了分隔两个有隙相的介观临界区域，在该区域内，关联先代数衰减，随后交叉为指数衰减。此外，纠缠熵在界面附近标度为涌现长度的对数，证实了介观临界区域的解释。我们的结果确立了一个普适临界长度，它支配着平滑拓扑界面的低能物理。
英文摘要：
Protected zero modes are a hallmark of topological phases of matter and are exponentially localized at sharp interfaces between distinct gapped phases. We investigate how this picture changes for smooth interfaces in a broad class of inhomogeneous Su-Schrieffer-Heeger (SSH) models. Combining an exact lattice solution with an inhomogeneous Dirac description, we show that the associated Jackiw-Rebbi zero mode becomes spatially extended. For arbitrary smooth hopping profiles, its lattice extension universally scales as the square root of the system size, independently of the microscopic details of the interface. This emergent length defines a mesoscopic critical region separating two gapped phases, within which correlations decay algebraically before crossing over to exponential decay. In addition, the entanglement entropy scales as the logarithm of the emergent length near the interface, confirming the interpretation of a mesoscopic critical region. Our results establish a universal critical length governing the low-energy physics of smooth topological interfaces.
