Precise Hamiltonian reconstruction from spectroscopy in magnets with competing interactions

Determine a precise procedure to infer the complete parameter set of a quantum magnet’s many-body spin Hamiltonian from spectroscopic measurements of spin excitations when multiple competing interactions are present and comparable in magnitude.

Background

Artificial quantum magnets realized with scanning probe microscopy allow spatially and energy-resolved spectroscopic measurements of spin excitations. These systems exhibit multiple interaction terms—such as isotropic Heisenberg exchange, anisotropic exchange, and Dzyaloshinskii–Moriya interaction—that can compete and produce similar spectral features, making it difficult to map measurements to Hamiltonian parameters.

The paper proposes a machine learning approach leveraging impurity-induced reconstructions to learn Hamiltonian parameters from dynamical correlators. The open question motivates the need for a robust, precise method to extract Hamiltonian parameters directly from spectroscopic data, especially in regimes where no single interaction dominates.

References

When engineering these artificial systems, a crucial open question is how the Hamiltonian of the system can be precisely obtained from spectroscopic measurements, especially in cases with multiple competing interactions.

— Hamiltonian learning quantum magnets with dynamical impurity tomography  (2510.18613 - Karjalainen et al., 21 Oct 2025) in Introduction

Can we reconstruct the spatially varying nearest-neighbor IXZ families studied here from all-zero input alone, up to Pauli-$Z$ conjugation and time reversal, with polynomial resource bounds under Gaussian smoothing?

— Out-of-control Hamiltonian Learning  (2610.06709 - Gong et al., 5 Oct 2026) in Section 6, Outlook, paragraph “Learning from all-zero input”