Observation of fractional edge excitations in nanographene spin chains

Abstract

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, solitons in one-dimensional conducting polymers and Majorana states in topological superconductors. 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 and, remarkably, S = 1/2 edge states at the chain termini, leading to a four-fold degenerate ground state that reflects the underlying symmetry-protected topological order. Here, we use on-surface synthesis to fabricate one-dimensional spin chains that contain the S = 1 polycyclic aromatic hydrocarbon triangulene as the building block. Using scanning tunneling 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 quantum spin liquid phases in purely organic materials, with the potential for the realization of measurement-based quantum computation.

23 pages, 4 main figures and 7 extended data figures; supplementary information containing additional data is included

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Cited by in corpus (21)

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• Quantum simulator to emulate lower dimensional molecular structure
• Addressing electron spins embedded in metallic graphene nanoribbons
• Construction of topological quantum magnets from atomic spins on surfaces
• Observation of competing, correlated ground states in the flat band of rhombohedral graphite
• Theory of triangulene two-dimensional crystals
• Preparing Valence-Bond-Solid states on noisy intermediate-scale quantum computers
• Pair-density-wave superconductor from doping Haldane chain and rung-singlet ladder
• Designing quantum many-body matter with conditional generative adversarial networks
• Hubbard model for spin-1 Haldane chains
• Electrically driven singlet-triplet transition in triangulene spin-1 chains
• Range of biquadratic and triquadratic Heisenberg effective couplings deduced from multiorbital Hubbard models
• Magnetic frustration and fractionalization in oligo(indenoindenes)
• Some aspects of Affleck-Kennedy-Lieb-Tasaki models: tensor network, physical properties, spectral gap, deformation, and quantum computation
• Network construction of non-Abelian chiral spin liquids
• Proximity-Induced Superconductivity in Atomically Precise Nanographene
• Quantum phase transition in magnetic nanographenes on a lead superconductor
• One-to-one correspondence between thermal structure factors and coupling constants of general bilinear Hamiltonians