Hamiltonian learning, triplons, and high-order topological order in engineered nanoscale quantum magnets

Atomic-scale quantum-magnets 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. First [1], we show that dynamical spin excitations provide a robust strategy to infer the nature of the underlying Hamiltonian, and to design artificial spin modes. 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. Second [2], we demonstrate the emergence of triplon excitations in an artificial atomic-scale magnet, exotic many-body modes emerging from propagating singlet-triplet transitions. These results provide a direct demonstration of dispersive triplon excitations from a real-space measurement. Third [3], we show that an engineered spin lattice allows creating a quantum spin liquid model featuring topological corner modes that stem from second-order many-body topological order. These results establish the first high-order topological quantum magnet realized experimentally. Finally [4], we will show how many-body methods based on tensor networks and neural network quantum states allow mapping the whole phase diagram of the frustrated topological quantum magnet we realized experimentally. Our results establish the potential of artificial nanoscale magnets to engineer quantum many body matter, and establish Hamiltonian learning as a powerful tool to design exotic artificial quantum magnets.

[1] Netta Karjalainen, Zina Lippo, Guangze Chen, Rouven Koch, Adolfo O. Fumega, and Jose L. Lado, Hamiltonian Inference from Dynamical Excitations in Confined Quantum Magnets, Phys. Rev. Applied 20, 024054 (2023)
[2] Robert Drost, Shawulienu Kezilebieke, Jose L. Lado, and Peter Liljeroth, Real-Space Imaging of Triplon Excitations in Engineered Quantum Magnets, Phys. Rev. Lett. 131, 086701 (2023)
[3] Hao Wang, Peng Fan, Jing Chen, Lili Jiang, Hong-Jun Gao, Jose L. Lado, Kai Yang, Construction of topological quantum magnets from atomic spins on surfaces, Nature Nanotechnology (2024), 10.1038/s41565-024-01775-2
[4] Pascal M. Vecsei, Jose L. Lado, Phase diagram of the J1-J2 Heisenberg second-order topological quantum magnet, arXiv:2408.16453 (2024)