Nonlinearity-induced Topological Phase Transitions in One-dimensional Systems with Chiral Symmetry: A Real-Space Treatment
Abstract
Nonlinearity can induce topological phase transitions in periodic systems. It is hence of considerable interest to examine if such transitions persist in the absence of translational symmetry. We address this question directly in real space, using the periodic Su-Schrieffer-Heeger (SSH) chain as a reference for understanding the effect of quasiperiodicity. How nonlinearity drives a chain towards a topological phase transition is found to depend strongly on the strength of the quasiperiodic potential. As the nonlinearity strength increases, we find that weak quasiperiodicity supports a transition from a trivial to a topological phase, whereas the intermediate regime does not have a topological phase transition. Under strong quasiperiodicity, pronounced boundary localization can develop well before a nonlinearity-induced topological transition. Our results show how nonlinearity may interplay with a quasiperiodic potential in inducing topological phase transitions and that boundary localization of nonlinear eigenstates alone may not be taken as a clear signature of topological edge states.
Related
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BibTeX
@misc{tao2026nonlinearityinduced,
title = {{Nonlinearity-induced Topological Phase Transitions in One-dimensional Systems with Chiral Symmetry: A Real-Space Treatment}},
author = {Liu Bi Tao and Shilpi Roy and Jiangbin Gong},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.04984},
eprint = {2610.04984},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.04984},
}
RIS
TY - UNPB
TI - Nonlinearity-induced Topological Phase Transitions in One-dimensional Systems with Chiral Symmetry: A Real-Space Treatment
AU - Liu Bi Tao
AU - Shilpi Roy
AU - Jiangbin Gong
PY - 2026
DA - 2026/10/04
PB - arXiv
DO - 10.48550/arxiv.2610.04984
UR - https://arxiv.org/abs/2610.04984
AB - Nonlinearity can induce topological phase transitions in periodic systems. It is hence of considerable interest to examine if such transitions persist in the absence of translational symmetry. We address this question directly in real space, using the periodic Su-Schrieffer-Heeger (SSH) chain as a reference for understanding the effect of quasiperiodicity. How nonlinearity drives a chain towards a topological phase transition is found to depend strongly on the strength of the quasiperiodic potential. As the nonlinearity strength increases, we find that weak quasiperiodicity supports a transition from a trivial to a topological phase, whereas the intermediate regime does not have a topological phase transition. Under strong quasiperiodicity, pronounced boundary localization can develop well before a nonlinearity-induced topological transition. Our results show how nonlinearity may interplay with a quasiperiodic potential in inducing topological phase transitions and that boundary localization of nonlinear eigenstates alone may not be taken as a clear signature of topological edge states.
ER -