  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.
