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Since longitudinal spin-spin interaction is ubiquitous in magnetic materials,it is very interesting to explore the interplay between topology andlongitudinal spin-spin interaction. Here, we examine the role of longitudinalspin-spin interaction on topological magnon excitations. Remarkably, even forsingle-magnon excitations, we discover topological edge states and defect edgestates of magnon excitations in a dimerized Heisenberg XXZ chain and theirtopological properties can be distinguished via adiabatic quantum transport. Weuncover topological phase transitions induced by longitudinal spin-spininteractions whose boundary is analytically obtained via the transfer matrixmethod. For multi-magnon excitations, even-magnon bound states are found to bealways topologically trivial, but odd-magnon bound states may be topologicallynontrivial due to the interplay between the transverse dimerization and thelongitudinal spin-spin interaction. For two-dimensional spin systems, thelongitudinal spin-spin interaction contributes to the coexistence of defectcorner states, second-order topological corner states and first-ordertopological edge states. Our work opens an avenue for exploring topologicalmagnon excitations and has potential applications in topological magnondevices.

Magnon boundary states tailored by longitudinal spin-spin interactions and topology