Hamiltonian learning quantum magnets with dynamical impurity tomography

Nanoscale engineered spin systems, ranging from spins on surfaces to nanographenes, provide flexible platforms to realize entangled quantum magnets from a bottom up approach. However, assessing the quantum many-body Hamiltonian realized in a specific experiment remains an exceptional open challenge, due to the difficulty of disentangling competing terms accounting for the many-body excitations. Here, we demonstrate a machine learning strategy to learn a quantum many-body spin Hamiltonian from scanning spectroscopy measurements of spin excitations. Our methodology leverages the spatially-resolved reconstruction of the many-body excitations induced by depositing quantum impurities next to the quantum magnet. We demonstrate that our algorithm allows us to predict long-range Heisenberg exchange interactions, anisotropic exchange, as well as antisymmetric Dzyaloshinskii-Moriya interaction, including in the presence of sizable noise. Our methodology establishes defect-induced spatially-resolved dynamical excitations in quantum magnets as a powerful strategy to understand the nature of quantum spin many-body models.