Universal scaling of spatially extended zero modes in inhomogeneous SSH chains

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.

Source: arXiv:2608.11021v1 - http://arxiv.org/abs/2608.11021v1 PDF: https://arxiv.org/pdf/2608.11021v1 Original Link: http://arxiv.org/abs/2608.11021v1