Nonlinearity-induced transition in nonlinear Su-Schrieffer-Heeger model and nonlinear higher-order topological system

TL;DR

This paper investigates how nonlinearity influences topological phases in nonlinear Schrödinger lattice systems, revealing a phase diagram with four distinct phases, including topological, trivial, localization, and dimer/trimer phases, through analytical and numerical methods.

Contribution

It provides the first detailed phase diagram of the nonlinear SSH model and extends the analysis to a higher-order topological system, identifying new nonlinear-induced phases.

Findings

Identified four phases in the nonlinear SSH model: topological, trivial, localization, and dimer phases.

Discovered a nonlinearity-induced localization phase at high nonlinearity levels.

Extended the analysis to a higher-order topological system, revealing a trimer phase.

Abstract

We study the topological physics in nonlinear Schr\"{o}dinger systems on lattices. We employ the quench dynamics to explore the phase diagram, where a pulse is given to a lattice point and we analyze its time evolution. There are two system parameters $\lambda $ and $\xi $, where $\lambda $ controls the hoppings between the neighboring links and $\xi $ controls the nonlinearity. The dynamics crucially depends on these system parameters. Based on analytical and numerical studies, we derive the phase diagram of the nonlinear Su-Schrieffer-Heeger (SSH) model in the ($\lambda ,\xi $) plane. It consists of four phases. The topological and trivial phases emerge when the nonlinearity $\xi $ is small. The nonlinearity-induced localization phase emerges when $\xi $ is large. We also find a dimer phase as a result of a cooperation between the hopping and nonlinear terms. A similar analysis is made of the nonlinear second-order topological system on the breathing Kagome lattice, where a trimer phase appears instead of the dimer phase.