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We explore the edge defects induced by spin-spin interaction in a finiteparadigmatic Heisenberg spin chain. By introducing a gradient magnetic fieldand a periodically-modulated spin-exchange strength, the resonance betweenmodulation frequency and magnetic field gradient can also induce asymmetricdefects at the edges, dubbed as Floquet-Wannier-Zeeman edge defects. Theinterplay between these two types of edge defects allows us to manipulate themagnon edge states from an isolated band into a continuum one. In thehigh-frequency regime, we analytically derive effective models to interpret theformation mechanisms for edge states by employing the multiscale perturbationanalysis. Our study offers new insights to understand and control the magnonedge states governed by the interplay between edge defects induced by thespin-spin interaction and the Floquet-Wannier-Zeeman manipulation.

Edge states in quantum spin chains: the interplay among interaction, gradient magnetic field and Floquet engineering