Topological Phases in Half-Integer Higher Spin J₁-J₂ Heisenberg Chains

We study the ground state properties of antiferromagnetic J₁-J₂ chains with half-integer spins ranging from S=32 to S=112 using the density-matrix renormalization group method. We map out the ground-state phase diagrams as a function of J₂J₁ containing topological phases with alternating 2S-12 and 2S+12 valence bonds. We identify these topological phases and their boundaries by calculating the string order parameter, the dimer order parameter, and the spin gap for those high-S systems in thermodynamic limit (finite size scaling). We find that these topological regions narrow down inversely with S and converge to a single point at J₂J₁=14 in the classical limit -- a critical threshold between commensurate and incommensurate orders. In addition, we extend the discussion of the Majumder-Ghosh state, previously noted only for S=12, and speculate its possible presence as a ground state in half-integer high spin systems over a substantial range of J₂J₁ values.