Engineering Biquadratic Interactions in Spin-1 Chains by Spin-1/2 Spacers

Low-dimensional quantum systems host a variety of exotic states, such as symmetry-protected topological ground states in spin-1 Haldane chains. Real-world realizations of such states could serve as practical quantum simulators for quantum phases if the interactions can be controlled. However, many proposed models, such as the AKLT state, require unconventional forms of spin interactions beyond standard Heisenberg terms, which do not naturally emerge from microscopic (Coulomb) interactions. Here, we demonstrate a general strategy to induce a biquadratic term between two spin-1 sites and to tune its strength $\beta$ by placing pairs of spin-1/2 spacers in between them. $\beta$ is controlled by the ratio between Heisenberg couplings to and in between the spacer spins. Increasing this ratio increases the magnitude of $\beta$ and decreases the correlation length of edge states, but at a critical value of the ratio, we observe a quantum phase transition between two spin-liquid phases with hidden antiferromagnetic order. Detailed atomistic calculations reveal that chains of nanographene flakes with 22 and 13 atoms, respectively, which could be realized by state-of-the-art bottom-up growth technology, yield precisely the couplings required to approach the AKLT state. These findings deliver a blueprint for engineering unconventional interactions in bottom-up synthesized quantum simulators.