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

Since longitudinal spin-spin interaction is ubiquitous in magnetic materials, it is very interesting to explore the interplay between topology and longitudinal spin-spin interaction. Here, we examine the role of longitudinal spin-spin interaction on topological magnon excitations. Remarkably, even for single-magnon excitations, we discover topological edge states and defect edge states of magnon excitations in a dimerized Heisenberg XXZ chain and their topological properties can be distinguished via adiabatic quantum transport. We uncover topological phase transitions induced by longitudinal spin-spin interactions whose boundary is analytically obtained via the transfer matrix method. For multi-magnon excitations, even-magnon bound states are found to be always topologically trivial, but odd-magnon bound states may be topologically nontrivial due to the interplay between the transverse dimerization and the longitudinal spin-spin interaction. For two-dimensional spin systems, the longitudinal spin-spin interaction contributes to the coexistence of defect corner states, second-order topological corner states and first-order topological edge states. Our work opens an avenue for exploring topological magnon excitations and has potential applications in topological magnon devices.