AI 中文总结
该研究探究含多拓扑畴壁的SSH链的输运性质，发现畴壁相互作用产生自相似分级光谱结构，通过递归构建有效SSH结构及重整化描述解释其起源，为一维系统的光谱设计提供新框架。
AI 中文摘要
我们研究了包含多个拓扑畴壁的Su-Schrieffer-Heeger（SSH）链的输运性质，结果表明这些畴壁的相互作用会产生一系列涌现的分级光谱结构。每个畴壁会在SSH能隙内贡献一个局域态，这些态的杂化会产生微带，其特征直接反映在透射谱中。通过结合具有不同畴壁间距的畴壁晶格，我们在微带子空间内构建了有效的SSH结构，所得透射谱再现了常规SSH链的特征，包括能隙形成、有限尺寸共振以及透射谱与能带结构的对应关系。该构建可递归应用，产生连续几代的有效SSH结构，因此有效SSH光谱会在逐渐变窄的能量区间内反复出现，形成微带和能隙的自相似分级结构。为理解该分级结构的起源，我们基于连续抽取发展了一种有效重整化描述，有效参数呈现出一系列交错的奇点，其数量在每次迭代中都会增加，这些奇点将能量轴划分为更精细的区间，为光谱的反复碎裂提供了自然解释。我们的结果表明，拓扑畴壁态可作为涌现自由度，用于设计多尺度输运通道、有效耦合和分级光谱结构；更广泛地说，本文引入的框架建立了一维系统中递归拓扑构造、有效哈密顿量与自相似光谱涌现之间的联系。
英文摘要
We investigate the transport properties of Su-Schrieffer-Heeger (SSH) chains containing multiple topological domain walls and show that their interaction generates a hierarchy of emergent spectral structures. Each domain wall contributes a localized state inside the SSH gap, and the hybridization of these states produces minibands whose signatures are directly reflected in the transmission spectra. By combining domain-wall lattices with different domain-wall separations, we construct effective SSH structures within the miniband subspace. The resulting transmission spectra reproduce the characteristic features of conventional SSH chains, including gap formation, finite-size resonances, and the correspondence between transmission spectra and band structure. The construction can be applied recursively, generating successive generations of effective SSH structures. As a consequence, effective SSH spectra repeatedly emerge within progressively narrower energy intervals, producing a self-similar hierarchy of minibands and spectral gaps. To understand the origin of this hierarchy, we develop an effective renormalized description based on successive decimation. The effective parameters exhibit a hierarchy of interlaced singularities whose number increases at each iteration. These singularities partition the energy axis into progressively finer intervals and provide a natural interpretation of the repeated fragmentation of the spectrum. Our results show that topological domain-wall states can act as emergent degrees of freedom from which multiscale transport channels, effective couplings, and hierarchical spectral structures may be engineered. More generally, the framework introduced here establishes a connection between recursive topological constructions, effective Hamiltonians, and the emergence of self-similar spectra in one-dimensional systems.
Comments23 pages, 7 figures
