Wave-packet spreading in the disordered and nonlinear Su-Schrieffer-Heeger chain

TL;DR

This study explores how wave-packets evolve over time in a disordered, nonlinear Su-Schrieffer-Heeger model, revealing the impact of topology and nonlinearity on wave spreading and localization.

Contribution

It demonstrates the transition from anomalous diffusion to localization in the linear regime and shows how nonlinearity alters wave dynamics in topological systems.

Findings

Anomalous diffusion occurs during topological phase transitions.

Nonlinearity suppresses anomalous diffusion, leading to uniform wave spreading.

Mode-mode interactions are crucial for understanding nonlinear topological phenomena.

Abstract

We numerically investigate the characteristics of the long-time dynamics of a single-site wave-packet excitation in a disordered and nonlinear Su-Schrieffer-Heeger model. In the linear regime, as the parameters controlling the topology of the system are varied, we show that the transition between two different topological phases is preceded by an anomalous diffusion, in contrast to Anderson localization within these topological phases. In the presence of on-site nonlinearity this feature is lost due to mode-mode interactions. Direct numerical simulations reveal that the characteristics of the asymptotic nonlinear wave-packet spreading are the same across the whole studied parameter space. Our findings underline the importance of mode-mode interactions in nonlinear topological systems, which must be studied in order to define reliable nonlinear topological markers.