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% 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.
Low-dimensional quantum magnets, particularly those with strong spin frustration, are characterized by their notable spin fluctuations. Nuclear magnetic resonance (NMR) serves as a sensitive probe of low-energy fluctuations that offers valuable insight into rich magnetic phases and emergent phenomena in quantum magnets. Although experimentally accessible, the numerical simulation of NMR relaxation rates, specifically the spin-lattice relaxation rate
1/T1, remains a significant challenge. Analytical continuation based on Monte Carlo calculations are hampered by the notorious negative sign for frustrated systems, and the real-time simulations incur significant costs to capture low-energy fluctuations. Here we propose computing the relaxation rate using thermal tensor networks (TTNs), which provides a streamlined approach by calculating its imaginary-time proxy. We showcase the accuracy and versatility of our methodology by applying it to one-dimensional spin chains and two-dimensional lattices, where we find that the critical exponents
η and
zν can be extracted from the low-temperature scalings of the simulated
1/T1 near quantum critical points. Our results also provide insights into the low-dimensional and frustrated magnetic materials, elucidating universal scaling behaviors in the Ising chain compound CoNb
2O
6 and revealing the renormalized classical behaviors in the triangular-lattice antiferromagnet Ba
8CoNb
6O
24. We apply the approach to effective model of the family of frustrated magnets AYbCh
2 (A = Na, K, Cs, and Ch = O, S, Se), and find dramatic changes from spin ordered to the proposed quantum spin liquid phase. Overall, with high reliability and accuracy, the TTN methodology offers a systematic strategy for studying the intricate dynamics observed across a broad spectrum of quantum magnets and related fields.
Thermal equilibrium states of many-body Hamiltonians are essential for probing quantum chaos, finite-temperature phases of matter, and training quantum machine learning models, yet generating large collections of such states across different Hamiltonians remains costly with existing methods. We introduce a powerful operation, the quantum thermal-drift channel, to construct a measurement-controlled sampling algorithm that autonomously generates thermal states together with their system Hamiltonians as labels for general physical models. We prove that our algorithm is efficient: the total gate count scales polynomially with system size and quadratically with inverse temperature, providing the first polynomial resource bound for random thermal state generation. We characterize the distribution of sampled Hamiltonians as a normal distribution reweighted by partition functions, which quantifies a trade-off between sampling accuracy and effective label range. Level-spacing statistics computed from sampled thermal states of a 2D transverse-field Ising model show a crossover to Wigner-Dyson universality, confirming that the sampler captures nontrivial chaotic correlations. Finally, a variational quantum classifier trained on the generated dataset achieves near-optimal accuracy in predicting Hamiltonian properties of unseen states. These results establish a scalable, quantum-native route for thermodynamic simulation and labeled quantum data generation in many-body systems.
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.
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.
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.