Emergence of quasiperiodic behavior in transport and hybridization properties of clean lattice systems

TL;DR

This paper demonstrates how quasiperiodic behavior can naturally emerge in clean, non-driven lattice systems, affecting localization, transport, and hybridization, with implications for experimental systems.

Contribution

It introduces a novel setting where quasiperiodicity arises without disorder or periodic driving, supported by two experimentally relevant examples.

Findings

Quasiperiodic behavior appears in clean lattice systems.

Localization and transport are influenced by emergent quasiperiodicity.

System geometry determines the number of localized states.

Abstract

Quasiperiodic behaviour is known to occur in systems with enforced quasiperiodicity or randomness, in either the lattice structure or the potential, as well as in periodically driven systems. Here, we present instead a setting where quasiperiodic behaviour emerges in clean, non-driven lattice systems. We illustrate this through two examples of experimental relevance, namely an infinite tight-binding chain with a gated segment, and a hopping particle coupled to static Ising degrees of freedom. We show how the quasiperiodic behaviour manifests in the number of states that are localised by the geometry of the system, with corresponding effects on transport and hybridisation properties.