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

TL;DR

This paper demonstrates that a single organic one-dimensional chain can host two distinct symmetry-protected topological phases, tunable via chemical modifications, with potential applications in nanoscale quantum devices.

Contribution

It introduces a chemically tunable organic chain hosting both odd-Haldane and Haldane phases, confirmed by theoretical and computational methods, advancing the realization of SPT phases in realistic systems.

Findings

Identification of two SPT phases in a single organic chain

Confirmation of SPT features via DMRG and exact diagonalization

Proposal of spectroscopic methods to detect Haldane states

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 odd-Haldane phase of a dimerized $S=\tfrac{1}{2}$ Heisenberg chain and a Haldane phase of an $S=1$ chain realized when Hund coupling locks two $S=\tfrac{1}{2}$ spins per monomer into $S=1$. Density-functional theory places the active manifold deep in the Mott regime ($U/t\!\approx\!126$), justifying a spin-only Heisenberg description; a compact $(t,U)\!\to\!J$ 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.