Latent Su-Schrieffer-Heeger models

TL;DR

This paper introduces latent SSH models with hidden symmetries that mimic topological features of traditional SSH chains, validated through experiments with electric circuits.

Contribution

It constructs new topological models with hidden reflection symmetry, expanding the understanding of topological phases beyond conventional symmetry constraints.

Findings

Latent SSH models exhibit multiple topological transitions.

They demonstrate quantized Zak phase despite lacking explicit symmetries.

Experimental validation confirms theoretical predictions.

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.