Tunable Topological Phases in an Organic One-Dimensional Mott Chain: Odd-Haldane (S = 1/2) and Haldane (S = 1)

Establishing symmetry-protected topological (SPT) phases with interactions in chemically realistic systems remains an open challenge. We show that a single, synthetically plausible organic one-dimensional chain, tunable via chemical modification of its radical sites, hosts two such phases: an odd-Haldane phase of a dimerized $S=\frac{1}{2}$ Heisenberg chain and a Haldane phase of an $S=1$ chain realized when Hund coupling locks two $S=\frac{1}{2}$ spins per monomer into $S=1$. Density-functional theory places the active manifold deep in the Mott regime ($U\mathrm{/}t\text{\hspace{0.17em}⁣}\approx \text{\hspace{0.17em}⁣}126$), justifying a spin-only Heisenberg description; a compact $(t,U)\text{\hspace{0.17em}⁣}\to \text{\hspace{0.17em}⁣}J$ mapping then fixes exchange couplings. Exact diagonalization and DMRG reveal a consistent SPT fingerprint across both phases, including a quantized many-body Zak phase, even-degenerate entanglement spectrum, protected edge spins, and characteristic triplon/Haldane features in $S^{+-}(q,\omega )$. Our results identify a chemically programmable molecular platform for interacting SPT physics in one dimension and suggest concrete spectroscopic routes to organic Haldane spin chains for nanoscale quantum devices.