Phase Diagram and Excitation Spectrum of S = 1 Antiferromagnetic Heisenberg Chains

Abstract

We investigate ground-state and low-lying excited states of the S = 1 antiferromagnetic Heisenberg chain with exchange anisotropy, single-ion anisotropy and biquadratic exchange and with free boundary conditions. We present an approximate mapping of the S = 1 model to an effective S = 1/2 chain in an external magnetic field, which can be solved exactly in several limiting cases. We obtain results for the phase diagram, correlation functions and the excitation spectrum. The transition to the Haldane phase is related to the condensation of the lowest soliton modes and the hidden order parameter of the Haldane phase is identified as transverse long-range order in the effective S = 1/2 chain.