Ground-State Phase Diagram and Magnetization Curves of the Spin-1 Antiferromagnetic Heisenberg Chain with Bond Alternation and Uniaxial Single-Ion-Type Anisotropy

Ground-state properties of the spin-1 antiferromagnetic Heisenberg chain with bond alternation and uniaxial single-ion-type anisotropy, which is described by the Hamiltonian \({ H}_0 = ∑₌₁^N\{1-(-1)^α\}{ S}_·{ S}₊₁ + D∑₌₁^N\;(S_^z)^2\) (0.0 ≤α≤1.0, -∞< D < ∞), are studied. An exact diagonalization method by means of the Lanczös technique is used. The ground-state phase diagram on the α versus D plane at the thermodynamic limit is determined by analyzing the Binder parameters associated with Néel order and z -direction string order for finite-size ( N = 6, 8, …, 16) chains. It is found that there exists a multicritical point at which the Haldane, Néel, and singlet-dimer phases meet and that the singlet-dimer phase and the large- D phase belong to the same unique phase. The ground-state magnetization curves at the thermodynamic limit for various values of α and D are obtained for the system described by the Hamiltonian, H 0 plus the Zeeman term - H ∑ ℓ=1 N S ℓ z . The results show that the 1/2-plateau appears in the magnetization curve at least when D ≥0.0 and \(0.0α ≤ 1.0\).