Latent Su-Schrieffer-Heeger models

• URL: http://arxiv.org/abs/2310.07619v1
• Date: Wed, 11 Oct 2023 16:00:21 GMT
• Title: Latent Su-Schrieffer-Heeger models
• Authors: Malte R\"ontgen, Xuelong Chen, Wenlong Gao, Maxim Pyzh, Peter Schmelcher, Vincent Pagneux, Vassos Achilleos, Antonin Coutant
• Abstract summary: Su-Schrieffer-Heeger (SSH) chain is the reference model of a one-dimensional topological insulator. Here, we harness recent graph-theoretical results to construct families of setups whose unit cell features neither of these symmetries. This causes the isospectral reduction -- akin to an effective Hamiltonian -- of the resulting lattice to have the form of an SSH model.
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• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: The Su-Schrieffer-Heeger (SSH) chain is the reference model of a one-dimensional topological insulator. Its topological nature can be explained by the quantization of the Zak phase, due to reflection symmetry of the unit cell, or of the winding number, due to chiral symmetry. Here, we harness recent graph-theoretical results to construct families of setups whose unit cell features neither of these symmetries, but instead a so-called latent or hidden reflection symmetry. This causes the isospectral reduction -- akin to an effective Hamiltonian -- of the resulting lattice to have the form of an SSH model. As we show, these latent SSH models exhibit features such as multiple topological transitions and edge states, as well as a quantized Zak phase. Relying on a generally applicable discrete framework, we experimentally validate our findings using electric circuits.

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