Construction of topological quantum magnets from atomic spins on surfaces

Artificial quantum systems have emerged as indispensable platforms to realize exotic topological matter in a well-controlled manner. Here, we demonstrate topological quantum Heisenberg spin lattices, engineered with spin chains and two-dimensional spin arrays using spin 1/2 atoms on insulating films in a scanning tunnelling microscope (STM). We engineered with atomic precision both topological and trivial phases of the quantum spin model, realizing first- and second-order topological quantum magnets. Their many-body excitations were probed by single-atom electron spin resonance with ultrahigh energy resolution. The atomically-localized magnetic field of the STM tip allows us to directly visualize various topological bound modes including topological edge states, topological defects, and higher-order corner modes. Our results provide an important bottom-up approach to simulating exotic quantum many-body phases of interacting spins.