Onset of incommensurability at the valence-bond-solid point in the S=1 quantum spin chain

Most of the present understanding of the S=1 quantum spin chains displaying the Haldane gap is coming from the so-called valence-bond-solid (VBS) Hamiltonian which has an exactly known ground state. We show that this point is characterized by the onset of short-range incommensurate spin correlations in the one-parameter family of Hamiltonians H-theta=COS theta Sigma(i)S(i) . S-i+1+sin theta Sigma(i)(S-i . S-i+1)(2). This gives a physical meaning to this special point. We establish precise values for the gaps, correlations, the string order parameter, and identify the VBS point as a disorder point in the sense of classical statistical mechanics. It is a quantum remnant of the classical transition between a ground state with long-range Neel order and a ground state with incommensurate long-range order.