Molecular Hamiltonian learning from setpoint-dependent scanning tunneling spectroscopy

TL;DR

This paper presents a machine learning method to extract microscopic Hamiltonian parameters of molecular quantum magnets from setpoint-dependent STM-IETS data, enabling quantitative atomic-scale characterization of quantum materials.

Contribution

It introduces molecular Hamiltonian learning, a novel approach that infers Hamiltonian parameters directly from experimental spectra using theoretical training data.

Findings

Successfully reconstructs Hamiltonian parameters from experimental spectra.

Demonstrates the method on iron phthalocyanine on SnTe surface.

Establishes a new automated strategy for quantum material characterization.

Abstract

Molecular quantum magnets adsorbed on surfaces exhibit rich spin and orbital excitations that can be probed by scanning tunneling microscopy with inelastic electron tunneling spectroscopy (STM-IETS). However, the quantitative extraction of the underlying multiorbital Hamiltonian from experimental spectra remains a fundamental challenge. Here, we introduce molecular Hamiltonian learning, a machine learning strategy that infers the microscopic Hamiltonian parameters of a single adsorbed molecule directly from the setpoint-dependence of STM-IETS data. The method leverages the systematic evolution of spectral features as the STM tip tunes the local electrostatic environment for different tip-sample distances. We demonstrate this approach on iron phthalocyanine on ferroelectric SnTe, training our algorithm on theory spectra from a realistic multiorbital model, including spin-orbit coupling, electrostatic interactions, local crystal field, and substrate effects. The algorithm, trained solely on theoretical many-body simulations, allows reconstructing Hamiltonian parameters directly from experimental spectra. Our manuscript establishes a flexible and automated strategy for Hamiltonian reconstruction from STM-IETS, transforming setpoint-dependent spectroscopy into quantitative characterization of quantum materials at the atomic scale.