Nonlinear Topological Edge States: from Dynamic Delocalization to Thermalization

TL;DR

This paper explores the nonlinear dynamics of topological edge states in a mechanical lattice, revealing how instability leads to chaos, thermalization, and a renormalized dispersion relation with unique symmetry properties.

Contribution

It introduces the study of nonlinear continuation of topological edge states and their long-term behavior, including chaos and thermalization, in a mechanical lattice model.

Findings

Linearly unstable edge states delocalize and cause chaos.

Stable edge states also thermalize after perturbation.

Thermalized states exhibit a symmetric, renormalized dispersion relation.

Abstract

We consider a mechanical lattice inspired by the Su-Schrieffer-Heeger model along with cubic Klein-Gordon type nonlinearity. We investigate the long-time dynamics of the nonlinear edge states, which are obtained by nonlinear continuation of topological edge states of the linearized model. Linearly unstable edge states delocalize and lead to chaos and thermalization of the lattice. Linearly stable edge states also reach the same fate, but after a critical strength of perturbation is added to the initial edge state. We show that the thermalized lattice in all these cases shows an effective renormalization of the dispersion relation. Intriguingly, this renormalized dispersion relation displays a unique symmetry, i.e., its square is symmetric about a finite squared frequency, akin to the chiral symmetry of the linearized model.