Shantanu Mishra, Gonçalo Catarina, Fupeng Wu, Ricardo Ortiz, David Jacob, Kristjan Eimre, Ji Ma, Carlo A. Pignedoli, Xinliang Feng, Pascal Ruffieux, Joaquín Fernández-Rossier, Roman Fasel

Fractionalization is a phenomenon in which strong interactions in a quantum system drive the emergence of excitations with quantum numbers that are absent in the building blocks. Outstanding examples are excitations with charge *e*/3 in the fractional quantum Hall effect^{1,2}, solitons in one-dimensional conducting polymers^{3,4} and Majorana states in topological superconductors^{5}. Fractionalization is also predicted to manifest itself in low-dimensional quantum magnets, such as one-dimensional antiferromagnetic *S* = 1 chains. The fundamental features of this system are gapped excitations in the bulk^{6} and, remarkably, *S* = 1/2 edge states at the chain termini^{7,8,9}, leading to a four-fold degenerate ground state that reflects the underlying symmetry-protected topological order^{10,11}. Here, we use on-surface synthesis^{12} to fabricate one-dimensional spin chains that contain the *S* = 1 polycyclic aromatic hydrocarbon triangulene as the building block. Using scanning tunnelling microscopy and spectroscopy at 4.5 K, we probe length-dependent magnetic excitations at the atomic scale in both open-ended and cyclic spin chains, and directly observe gapped spin excitations and fractional edge states therein. Exact diagonalization calculations provide conclusive evidence that the spin chains are described by the *S* = 1 bilinear-biquadratic Hamiltonian in the Haldane symmetry-protected topological phase. Our results open a bottom-up approach to study strongly correlated phases in purely organic materials, with the potential for the realization of measurement-based quantum computation^{13}.