Tunable Topological Phases in an Organic One-Dimensional Mott Chain: Exchange-Alternating <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>S</mi><mo>=</mo><mfrac><mrow><mn>1</mn></mrow><mrow><mn>2</mn></mrow></mfrac></math> and Haldane <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>S</mi><mo>=</mo><mrow><mn>1</mn></mrow></math>.

Abstract

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 even-Haldane phase of a dimerized <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>S</mi><mo>=</mo><mfrac><mrow><mn>1</mn></mrow><mrow><mn>2</mn></mrow></mfrac></math> Heisenberg chain and a Haldane phase of an <i>S</i> = 1 chain realized when Hund coupling locks two <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>S</mi><mo>=</mo><mfrac><mrow><mn>1</mn></mrow><mrow><mn>2</mn></mrow></mfrac></math> spins per monomer into <i>S</i> = 1. Density-functional theory places the active manifold deep in the Mott regime (<i>U</i>/<i>t</i> > 100), justifying a spin-only Heisenberg description; a compact (<i>t</i>,<i>U</i>) → <i>J</i> 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 <i>S</i>^+-(<i>q</i>,ω). 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.