Hamiltonian inference from dynamical excitations in spin quantum dots

Quantum-disordered models provide a versatile platform to explore the emergence of quantum excitations in many-body systems. The engineering of spin models at the atomic scale with scanning tunneling microscopy and the local imaging of excitations with electrically driven spin resonance has risen as a powerful strategy to image spin excitations in finite quantum spin systems. Here, focusing on $S=1/2$ lattices as realized by TiH in MgO, we show that dynamical spin excitations provide a robust strategy to infer the nature of the underlying Hamiltonian. We show that finite-size interference of the dynamical many-body spin excitations of a generalized long-range Heisenberg model allows the underlying spin couplings to be inferred. We show that the spatial distribution of local spin excitations in TiH islands and ladders directly correlates with the underlying ground state in the thermodynamic limit. Using a supervised learning algorithm, we demonstrate that the different parameters of the Hamiltonian can be extracted by providing the spatially and frequency-dependent local excitations that can be directly measured by electrically driven spin resonance with scanning tunneling microscopy. Our results put forward local dynamical excitations in confined quantum spin models as versatile witnesses of the underlying ground state, providing an experimentally robust strategy for Hamiltonian inference in complex real spin models.