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arXiv:2510.23555 · SciPost Physics

Two topological phases in exchange alternating spin-1 nanographene chains

J. C. G. Henriques, Y. del Castillo, Ricardo Segundo, Jan Phillips, Joaquín Fernández-Rossier

Published Jul 7, 2026• 2 citations
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Abstract

Magnetic nanographenes are emerging as versatile building blocks for artificial spin lattices, enabling the exploration of flagship one-dimensional quantum-magnetism models with unprecedented control. The spin-1 Heisenberg model, including bilinear and biquadratic exchange, was first realized using [3]-triangulenes, revealing the Haldane phase. More recently, Clar’s goblets enabled the spin-1/2 Heisenberg model with exchange alternation, uncovering additional topological phases. Here we show that spin-1 nanographenes can be used to explore bond-alternating chains both in the Haldane phase and beyond it, in a dimerized phase with emergent edge spin-1. We use density matrix renormalization group (DMRG) to analyze how biquadratic exchange, which is known to be large in spin-1 nanographenes, determines the phase transition boundary. Combining multiconfigurational and first-principles calculations, we identify two realistic candidates to realize these two different phases: the recently synthesized extended Clar’s goblet and a passivated [4]-triangulene. We demonstrate how to distinguish these phases experimentally using inelastic electron tunneling spectroscopy, paving the way for their observation.

DOI
10.21468/scipostphys.21.1.009

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Magnetic nanographenes are emerging as versatile building blocks for artificial spin lattices, enabling the exploration of flagship one-dimensional quantum-magnetism models with unprecedented control. The spin-1 Heisenberg model, including bilinear and biquadratic exchange, was first realized using [3]-triangulenes, revealing the Haldane phase. More recently, Clar’s goblets enabled the spin-1/2 Heisenberg model with exchange alternation, uncovering additional topological phases. Here we show that spin-1 nanographenes can be used to explore bond-alternating chains both in the Haldane phase and beyond it, in a dimerized phase with emergent edge spin-1. We use density matrix renormalization group (DMRG) to analyze how biquadratic exchange, which is known to be large in spin-1 nanographenes, determines the phase transition boundary. Combining multiconfigurational and first-principles calculations, we identify two realistic candidates to realize these two different phases: the recently synthesized extended Clar’s goblet and a passivated [4]-triangulene. We demonstrate how to distinguish these phases experimentally using inelastic electron tunneling spectroscopy, paving the way for their observation.
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Antiferromagnetic spin-1 chains host the celebrated symmetry-protected topological Haldane phase, whose spin-1/21/21/2 edge states were evidenced in bulk by, e.g., electron spin resonance (ESR). To fully reveal and manipulate the spin-1/21/21/2 degree of freedom, one may build on the recent success in assembling effective spin-1 antiferromagnetic chains from nanographene and porphyrin molecules, and on the nascent technique of combined ESR and scanning tunneling microscopy, which is able to measure the spin dynamics site by site with atomic real-space resolution. In this Letter, we combine exact diagonalization and density matrix renormalization group to investigate the local dynamic spin structure factor of the different phases of the bilinear-biquadratic Hamiltonian with single-ion anisotropy in the presence of an external magnetic field. We find that the signature of the Haldane phase is a low-energy peak created by singlet-triplet transitions in the edge-state manifold. We predict that the signature peak is experimentally observable, although for chains of length above N=30N=30N=30 its energy should be first tuned by application of an external magnetic field. We fully characterize the peak in real space and energy, and further show its robustness to weak anisotropy and a relevant range of temperatures.
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