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

Abstract

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 ${\mathit{H}}_{\mathrm{\ensuremath{\theta}}}$= cos\ensuremath{\theta}${\ensuremath{\sum}}_{\mathit{i}}$${\mathit{S}}_{\mathit{i}}$\ensuremath{\cdot}${\mathit{S}}_{\mathit{i}+1}$+sin\ensuremath{\theta}${\ensuremath{\sum}}_{\mathit{i}}$ (${\mathit{S}}_{\mathit{i}}$\ensuremath{\cdot}${\mathit{S}}_{\mathit{i}+1}$${)}^{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 N\'eel order and a ground state with incommensurate long-range order. \textcopyright{} 1996 The American Physical Society.