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Quantum-disordered models provide a versatile platform to explore theemergence of quantum excitations in many-body systems. The engineering of spinmodels at the atomic scale with scanning tunneling microscopy and the localimaging of excitations with electrically driven spin resonance has risen as apowerful strategy to image spin excitations in finite quantum spin systems.Here, focusing on $S=1/2$ lattices as realized by Ti in MgO, we show thatdynamical spin excitations provide a robust strategy to infer the nature of theunderlying Hamiltonian. We show that finite-size interference of the dynamicalmany-body spin excitations of a generalized long-range Heisenberg model allowsthe underlying spin couplings to be inferred. We show that the spatialdistribution of local spin excitations in Ti islands and ladders directlycorrelates with the underlying ground state in the thermodynamic limit. Using asupervised learning algorithm, we demonstrate that the different parameters ofthe Hamiltonian can be extracted by providing the spatially andfrequency-dependent local excitations that can be directly measured byelectrically driven spin resonance with scanning tunneling microscopy. Ourresults put forward local dynamical excitations in confined quantum spin modelsas versatile witnesses of the underlying ground state, providing anexperimentally robust strategy for Hamiltonian inference in complex real spinmodels.

Hamiltonian inference from dynamical excitations in confined quantum magnets