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 superconductors⁵. 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 bulk⁶ 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 synthesis¹² 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 computation¹³.

分馏是一种现象，在这种现象中，量子系统中的强相互作用会驱动出现具有构建块中不存在的量子数的激发。突出的例子是分数量子霍尔效应^{1,2中带电荷}e /3 的激发、一维导电聚合物中的孤子^3,4和拓扑超导体⁵中的马约拉纳态。预计分馏也会在低维量子磁体中表现出来，例如一维反铁磁S  = 1 链。该系统的基本特征是体积⁶中的间隙激发，并且值得注意的是， 链末端的S = 1/2 边缘状态^7,8,9，导致四重退化基态，反映了潜在的对称保护拓扑顺序^10,11。在这里，我们使用表面合成¹²来制造包含S  = 1 多环芳烃三角烯作为构建块的一维自旋链。在 4.5 K 下使用扫描隧道显微镜和光谱学，我们在开放式和循环自旋链中探测原子尺度的长度依赖性磁激发，并直接观察其中的带隙自旋激发和分数边缘态。精确的对角化计算提供了自旋链由S描述的确凿证据 = 1 个双线性双二次哈密顿量，在 Haldane 对称保护拓扑相中。我们的结果开启了一种自下而上的方法来研究纯有机材料中的强相关相，具有实现基于测量的量子计算¹³的潜力。