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

Abstract

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. We propose an experimental scheme to realize and measure the magnon boundary states in superconducting qubits. Our work opens an avenue for exploring topological magnon excitations and has potential applications in topological magnon devices.