Parity-dependent reentrant topology in a Su--Schrieffer--Heeger chain with power-law quasiperiodic modulation
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arXiv
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2026
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| _version_ | 1866911638616014848 |
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| author | Niu, Yusheng Liu, Hui Xu, Zhihao |
| author_facet | Niu, Yusheng Liu, Hui Xu, Zhihao |
| contents | We investigate reentrant topological transitions in a one-dimensional Su--Schrieffer--Heeger chain with power-law quasiperiodically modulated intracell hopping. The modulation is characterized by a positive integer exponent $n$ and a tunable parameter $β$, which continuously interpolates between the smooth power-law quasiperiodic limit and a sign-function limit that becomes square-wave-like for odd $n$ and uniform for even $n$. By combining analytical calculations of the zero-mode inverse localization length with numerical evaluations of a real-space topological indicator, we determine the topological phase diagrams in the $β\to 0$, $β\to\infty$, and finite-$β$ regimes. We show that deterministic quasiperiodic modulation can induce TAI-like reentrant topological phases within finite parameter windows. The formation of these phases depends crucially on the parity of $n$: for positive modulation strength, odd-power modulations can induce reentrant topology from the clean trivial regime $|t_1|>1$, whereas even-power modulations allow such reentrance only from the negative clean trivial regime $t_1<-1$. Exact analytical expressions for the zero-mode inverse localization length are obtained for $n=1,2,3,4$, yielding explicit or implicit transition conditions. The finite-$β$ results demonstrate that the parity-dependent structure remains robust throughout the interpolation between the two limiting cases. This parity effect originates from whether the modulation preserves or removes the sign structure of $\cos x$. We further propose an electrical-circuit implementation and discuss experimentally accessible signatures of the reentrant trivial--topological--trivial transition. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2605_00543 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Parity-dependent reentrant topology in a Su--Schrieffer--Heeger chain with power-law quasiperiodic modulation Niu, Yusheng Liu, Hui Xu, Zhihao Disordered Systems and Neural Networks We investigate reentrant topological transitions in a one-dimensional Su--Schrieffer--Heeger chain with power-law quasiperiodically modulated intracell hopping. The modulation is characterized by a positive integer exponent $n$ and a tunable parameter $β$, which continuously interpolates between the smooth power-law quasiperiodic limit and a sign-function limit that becomes square-wave-like for odd $n$ and uniform for even $n$. By combining analytical calculations of the zero-mode inverse localization length with numerical evaluations of a real-space topological indicator, we determine the topological phase diagrams in the $β\to 0$, $β\to\infty$, and finite-$β$ regimes. We show that deterministic quasiperiodic modulation can induce TAI-like reentrant topological phases within finite parameter windows. The formation of these phases depends crucially on the parity of $n$: for positive modulation strength, odd-power modulations can induce reentrant topology from the clean trivial regime $|t_1|>1$, whereas even-power modulations allow such reentrance only from the negative clean trivial regime $t_1<-1$. Exact analytical expressions for the zero-mode inverse localization length are obtained for $n=1,2,3,4$, yielding explicit or implicit transition conditions. The finite-$β$ results demonstrate that the parity-dependent structure remains robust throughout the interpolation between the two limiting cases. This parity effect originates from whether the modulation preserves or removes the sign structure of $\cos x$. We further propose an electrical-circuit implementation and discuss experimentally accessible signatures of the reentrant trivial--topological--trivial transition. |
| title | Parity-dependent reentrant topology in a Su--Schrieffer--Heeger chain with power-law quasiperiodic modulation |
| topic | Disordered Systems and Neural Networks |
| url | https://arxiv.org/abs/2605.00543 |