Nonlinear topological phase transitions in the dimerized sine-Gordon model

We investigate the topological physics and nonlinearity-induced trap phenomenon in a coupled system of pendulums. It is described by dimerized sine-Gordon model, which combination model Su-Schrieffer-Heeger model. The initial swing angle left-end pendulum may be regarded as nonlinearity parameter. number well defined far approximated harmonic oscillator. emergence edge state clearly observable phase solving quench dynamics starting from pendulum. A diagram constructed space $\xi \pi $ with $|\xi |\leq 1$ dimerization parameter $\lambda $|\lambda 1$. found that boundary rather insensitive to for $% |\xi |\lesssim 1/2$. On other hand, effect becomes dominant |\gtrsim 1/2$, eventually turns into phase. Furthermore, when almost ($\lambda \simeq 1$), standing waves appear are trapped few pendulums at left-end, forming dimer Its dynamical origin cooperation nonlinear term.