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

We study the topological physics in nonlinear Schrödinger 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 λ and ξ , where λ controls the hoppings between the neighboring links and ξ 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 (λ ,ξ ) plane. It consists of four phases. The topological and trivial phases emerge when the nonlinearity ξ is small. The nonlinearity-induced localization phase emerges when ξ 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.