Dual-mapping and quantum criticality in off-diagonal Aubry-Andr\'{e} models

TL;DR

This paper investigates off-diagonal quasiperiodic hopping models based on the Su-Schrieffer-Heeger chain, revealing a dual-mapping relation and the emergence of quantum criticality over a broad parameter space, offering new insights into quasiperiodic systems.

Contribution

It introduces a dual-mapping relation in off-diagonal quasiperiodic models and demonstrates the presence of quantum criticality, expanding understanding beyond diagonal quasiperiodic systems.

Findings

Dual-mapping relation in parameter space of the model

Quantum criticality can emerge and persist over a wide parameter range

Distinctive properties compared to diagonal quasiperiodic systems

Abstract

We study a class of off-diagonal quasiperiodic hopping models described by one-dimensional Su-Schrieffer-Heeger chain with quasiperiodic modulations. We unveil a general dual-mapping relation in parameter space of the dimerization strength $\lambda$ and the quasiperiodic modulation strength $V$, regardless of the specific details of the quasiperiodic modulation. Moreover, we demonstrated semi-analytically and numerically that under the specific quasiperiodic modulation, quantum criticality can emerge and persist in a wide parameter space. These unusual properties provides a distinctive paradigm compared with the diagonal quasiperiodic systems.