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arXiv:2606.29281

Learning Inhomogeneous Heisenberg Hamiltonians in Nanographene Spin Chains

Greta Lupi, Saketh Ravuri, Chenxiao Zhao, Weidan Zhang, Cesare Roncaglia, Renxiang Liu, Xinliang Feng, Daniele Passerone, Pascal Ruffieux, Roman Fasel, Jose L. Lado, Gonçalo Catarina

cond-mat.mes-hallquant-phSubmitted Jun 28, 2026• Announced Jun 30, 2026• 0 citations
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Abstract

Inferring microscopic Hamiltonians from experimental data is a central challenge in quantum materials and quantum simulation. In low-dimensional spin systems, exchange interactions are often assumed to be spatially uniform, despite structural and environmental inhomogeneities that can locally modify the coupling. Here, we leverage a local, length-independent machine learning methodology to reconstruct spatially modulated exchange interactions directly from inelastic scanning tunneling spectroscopy maps. We demonstrate this approach with nanographene spin chains, identifying both near-uniform and inhomogeneous regimes across the synthesized magnets. The reconstructed models quantitatively reproduce the experimental spectra and recover the correct scaling of the excitation gap with system size. Our results establish a general strategy to bridge local spectroscopic measurements with effective many-body Hamiltonians.

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22 pages, 34 figures

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Inferring microscopic Hamiltonians from experimental data is a central challenge in quantum materials and quantum simulation. In low-dimensional spin systems, exchange interactions are often assumed to be spatially uniform, despite structural and environmental inhomogeneities that can locally modify the coupling. Here, we leverage a local, length-independent machine learning methodology to reconstruct spatially modulated exchange interactions directly from inelastic scanning tunneling spectroscopy maps. We demonstrate this approach with nanographene spin chains, identifying both near-uniform and inhomogeneous regimes across the synthesized magnets. The reconstructed models quantitatively reproduce the experimental spectra and recover the correct scaling of the excitation gap with system size. Our results establish a general strategy to bridge local spectroscopic measurements with effective many-body Hamiltonians.
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Unlocking the potential of topological order within many-body spin systems has long been a central pursuit in the realm of quantum materials. Despite extensive efforts, the quest for a versatile platform enabling site-selective spin manipulation, essential for tuning and probing diverse topological phases, has persisted. Here, we utilize on-surface synthesis to construct spin-1/2 alternating-exchange Heisenberg (AH) chains[1] with antiferromagnetic couplings J1J_1J1​ and J2J_2J2​ by covalently linking Clar's goblets -- nanographenes each hosting two antiferromagnetically-coupled unpaired electrons[2]. Utilizing scanning tunneling microscopy, we exert atomic-scale control over the spin chain lengths, parities and exchange-coupling terminations, and probe their magnetic response by means of inelastic tunneling spectroscopy. Our investigation confirms the gapped nature of bulk excitations in the chains, known as triplons[3]. Besides, the triplon dispersion relation is successfully extracted from the spatial variation of tunneling spectral amplitudes. Furthermore, depending on the parity and termination of chains, we observe varying numbers of in-gap S=1/2S=1/2S=1/2 edge spins, enabling the determination of the degeneracy of distinct topological ground states in the thermodynamic limit-either 1, 2, or 4. By monitoring interactions between these edge spins, we identify the exponential decay of spin correlations. Our experimental findings, corroborated by theoretical calculations, present a phase-controlled many-body platform, opening promising avenues toward the development of spin-based quantum devices.
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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=1/2S=1/2S=1/2 lattices as realized by Ti\mathrm{Ti}Ti in MgO\mathrm{Mg}\mathrm{O}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 Ti\mathrm{Ti}Ti 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 dependent 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.