Matryoshka approach to sine-cosine topological models
نویسندگان
چکیده
We address a particular set of extended Su-Schrieffer-Heeger models with $2n$ sites in the unit cell [SSH($2n$)], that we designate by Sine-Cosine [SC$(n)$], hopping terms defined as sequence $n$ sine-cosine pairs form $\{\sin(\theta_j),\cos(\theta_j)\}$, $j=1, \cdots,n$. These models, when squared, generate block-diagonal matrix representation one blocks corresponding to chain uniform local potentials. further focus our study on subset SC$(2^{n-1})$ chains that, squared an arbitrary number times (up $n$), always block which is again model, if energy shift applied and renormalized. show these $n$-times squarable [SSC$(n)$] their band structure are uniquely determined renormalizations shifts associated each step squaring process. Chiral symmetry present all edge states levels at respective central gaps protected it. Zero-energy SSC$(j)$ (with $j<n$) Matryoshka obtained SSC$(n)$ open boundary conditions (OBC), become finite non-central chain. The extension higher dimensions discussed.
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ژورنال
عنوان ژورنال: Physical Review B
سال: 2021
ISSN: ['1098-0121', '1550-235X', '1538-4489']
DOI: https://doi.org/10.1103/physrevb.103.245112