Transition from topological to chaos in the nonlinear Su-Schrieffer-Heeger model

Recent studies on topological insulators have expanded into the nonlinear regime, while the bulk-edge correspondence in strongly nonlinear systems has been unelucidated. Here, we reveal that nonlinear topological edge modes can exhibit a transition to spatial chaos by increasing nonlinearity, which can be a universal mechanism of the breakdown of the bulk-edge correspondence. Specifically, we unveil the underlying dynamical system describing the spatial distribution of zero modes and show the emergence of chaos. We also propose the correspondence between the absolute value of the topological invariant and the dimension of the stable manifold under sufficiently weak nonlinearity. Our results provide a general guiding principle to investigate the nonlinear bulk-edge correspondence that can potentially be extended to arbitrary dimensions.