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Työväentutkimus Vuosikirja

Hamiltonian parameter learning in one-dimensional spin chains with machine learning

Netta Karjalainen

Published Mar 20, 2025• 0 citations
OpenAlex

Abstract

One-dimensional quantum spin chains provide a versatile platform for design of artificial quantum matter that enables breakthroughs in spintronics and quantum computing. These spin systems can be engineered at the atomic scale with scanning tunneling microscopy and their local excitations can be measured with electrically driven spin resonance. When engineering these system, a major open challenge is to extract parameters of the many-body spin Hamiltonian, since the extraction must be done indirectly. This thesis presents a machine learning technique that allows to infer the underlying Hamiltonian parameters via dynamical spin excitations. The methodology is based on the exploitation of many-body reconstructions around engineered quantum impurities adjacent to S=1/2 spin chains. These systems can be realized by hydrogenated titanium atoms in magnesium oxide films, featuring S=1/2 impurities next to the chain. The presented supervised methodology exploits the local dynamical correlator functions to provide the full many-body Hamiltonian as a result. Two neural networks using different quantum impurity placements are implemented. The networks allow to predict long range Heisenberg exchange interactions J2 and J3, anisotropic exchange interaction JZ, as well as antisymmetric Dzyaloshinskii-Moriya exchange interaction JDMI accurately for spin chain with a length of 21 spins from computational data. It is demonstrated that the approach is robust to noise in the spin excitations, offering an experimentally realistic strategy for Hamiltonian learning. It is also shown that different impurity placements offer better estimates for the parameters. With further research, the networks could be used to predict the parameters from experimental data. The introduced technique demonstrates the applicability of machine learning methodology to study nano-scale quantum systems and puts forward confined excitations in quantum magnets as a powerful strategy to understand the nature of quantum spin many-body models.

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One-dimensional quantum spin chains provide a versatile platform for design of artificial quantum matter that enables breakthroughs in spintronics and quantum computing. These spin systems can be engineered at the atomic scale with scanning tunneling microscopy and their local excitations can be measured with electrically driven spin resonance. When engineering these system, a major open challenge is to extract parameters of the many-body spin Hamiltonian, since the extraction must be done indirectly. This thesis presents a machine learning technique that allows to infer the underlying Hamiltonian parameters via dynamical spin excitations. The methodology is based on the exploitation of many-body reconstructions around engineered quantum impurities adjacent to S=1/2 spin chains. These systems can be realized by hydrogenated titanium atoms in magnesium oxide films, featuring S=1/2 impurities next to the chain. The presented supervised methodology exploits the local dynamical correlator functions to provide the full many-body Hamiltonian as a result. Two neural networks using different quantum impurity placements are implemented. The networks allow to predict long range Heisenberg exchange interactions J2 and J3, anisotropic exchange interaction JZ, as well as antisymmetric Dzyaloshinskii-Moriya exchange interaction JDMI accurately for spin chain with a length of 21 spins from computational data. It is demonstrated that the approach is robust to noise in the spin excitations, offering an experimentally realistic strategy for Hamiltonian learning. It is also shown that different impurity placements offer better estimates for the parameters. With further research, the networks could be used to predict the parameters from experimental data. The introduced technique demonstrates the applicability of machine learning methodology to study nano-scale quantum systems and puts forward confined excitations in quantum magnets as a powerful strategy to understand the nature of quantum spin many-body models.
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, and 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.
Impurities in quantum materials have provided successful strategies for learning properties of complex states, ranging from unconventional superconductors to topological insulators. In quantum magnetism, inferring the Hamiltonian of an engineered system becomes a challenging open problem in the presence of complex interactions. Here we show how a supervised machine-learning technique can be used to infer Hamiltonian parameters from atomically engineered quantum magnets by inferring fluctuations of the ground states due to the presence of impurities. We demonstrate our methodology both with a fermionic model with spin-orbit coupling, as well as with many-body spin models with long-range exchange and anisotropic exchange interactions. We show that our approach enables performing Hamiltonian extraction in the presence of significant noise, providing a strategy to perform Hamiltonian learning with experimental observables in atomic-scale quantum magnets. Our results establish a strategy to perform Hamiltonian learning by exploiting the impact of impurities in complex quantum many-body states.
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.
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.
High Resolution Image Download MS PowerPoint Slide Extracting the Hamiltonian parameters of nanoscale quantum magnets from experimental measurements is a significant challenge in quantum matter. Here we establish a machine learning strategy to extract the parameters of a spin Hamiltonian from inelastic spectroscopy with scanning tunneling microscopy, and we demonstrate this methodology experimentally with an artificial nanoscale molecular magnet based on cobalt phthalocyanine (CoPC) molecules on NbSe 2 . We show that this technique allows us to extract the Hamiltonian parameters of a quantum magnet from the differential conductance, including the substrate-induced spatial variation of the exchange couplings. Our methodology leverages a machine learning algorithm trained on exact quantum many-body simulations with tensor networks of finite quantum magnets, leading to a methodology that predicts the Hamiltonian parameters of CoPC quantum magnets of arbitrary size. Our results demonstrate how quantum many-body methods and machine learning enable us to learn a microscopic description of nanoscale quantum many-body systems with scanning tunneling spectroscopy.
Determining the microscopic Hamiltonian of a quantum magnet from inelastic neutron scattering measurements remains a central challenge in condensed matter physics. While the dynamical spin structure factor contains, in principle, sufficient information about the underlying interactions, extracting Hamiltonian parameters from experimental spectra constitutes a highly nontrivial inverse problem due to the large parameter space and the presence of experimental noise. Here we demonstrate that neural networks can efficiently solve this inverse problem for a broad class of quantum magnets. As a benchmark, we consider an eight-parameter family of honeycomb lattice Heisenberg spin models in the fully polarized phase, where the dynamical spin structure factor can be computed exactly within linear spin-wave theory. Using a large synthetic dataset of neutron scattering spectra, we train neural networks to infer the underlying Hamiltonian parameters directly from the dynamical response. We compare the performance of three different architectures---fully connected neural networks (FCNNs), one-dimensional convolutional neural networks (CNN1Ds), and two-dimensional convolutional neural networks (CNN2Ds)---and find that all achieve high predictive accuracy. Remarkably, the trained models remain robust in the presence of substantial experimental uncertainty, reliably recovering the Hamiltonian parameters even when the input spectra are contaminated by random noise with amplitudes reaching 10%10\%10% of the signal intensity. Our results establish machine learning as a powerful framework for quantitative Hamiltonian reconstruction from neutron scattering data and provide a practical route toward automated characterization of quantum magnetic materials.