Stability of topologically protected edge states in nonlinear quantum walks: Additional bifurcations unique to Floquet systems

Abstract

Recently, effects of nonlinearity on topologically nontrivial systems have attracted attention and the stability of topologically protected edge states has been studied for a quantum walk with nonlinear effects, which is akin to time-periodically driven systems (Floquet systems). In the previous work, it has been found that the edge states can be stable attractors or unstable repellers depending on their intrinsic topological property, while the stability is not affected by the strength of nonlinearity. In the present work, we find additional bifurcations at which edge states change from stable attractors to unstable repellers with increasing the strength of nonlinearity in nonlinear quantum walks, for the first time. The new bifurcations are unique to Floquet systems, since we take dynamical properties of Floquet systems into consideration by directly applying the time-evolution operator of the quantum walks to the linear stability analysis. Our results shed new light on nonlinear effects on topological edge states in Floquet systems.

28 pages, 11 figures

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Cited by in corpus (9)

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• Topological Protection in a Strongly Nonlinear Interface Lattice
• Topological Quantum Walk with Discrete Time-Glide Symmetry
• Fate of Topological Edge States in Disordered Periodically-driven Nonlinear Systems
• Nonlinear Topological Edge States: from Dynamic Delocalization to Thermalization
• Asymptotic stability of small bound state of nonlinear quantum walks
• Logarithmic expansion of many-body wave packets in random potentials
• Dynamical nonlinear optical response in time-periodic quantum systems
• Topological Phase Transitions and Edge-State Transfer in Time-Multiplexed Quantum Walks