By using mainly numerical methods, we investigate the ground-state phase diagram (GSPD) of an
S=1 ferromagnetic-antiferromagnetic bond-alternating chain with the
XXZ and the on-site anisotropies. This system can be mapped onto an anisotropic spin-2 chain when the ferromagnetic interaction is much stronger than the antiferromagnetic interaction. Since there are many quantum parameters in this system, we numerically obtained the GSPD on the plane of the magnitude of the antiferromagnetic coupling versus its
XXZ anisotropy, by use of the exact diagonalization, the level spectroscopy as well as the phenomenological renormalization group. The obtained GSPD consists of six phases. They are the $XY
1,thelarge−D$ (LD), the intermediate-
D (ID), the Haldane (H), the spin-1 singlet dimer (SD), and the Néel phases. Among them, the LD, the H, and the SD phases are the trivial phases, while the ID phase is the symmetry-protected topological phase. The former three are smoothly connected without any quantum phase transitions. It is also emphasized that the ID phase appears in a wider region compared with the case of the GSPD of the anisotropic spin-2 chain with the
XXZ and the on-site anisotropies. We also compare the obtained GSPD with the result of the perturbation theory.
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 \({\cal H}_0 = \sum_{\ell=1}^N\{1-(-1)^\ell\alpha\}{\mib S}_\ell\cdot{\mib S}_{\ell+1} + D\sum_{\ell=1}^N\;(S_\ell^z)^2\) (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
0.0≲α≤1.0.
The ground-state phase diagram of
S=2 antiferromagnetic Heisenberg chains with coexisting uniform and alternating single-site anisotropies is investigated by the numerical exact diagonalization and density matrix renormalization group methods. We find the Haldane, large-
D, Néel, period-doubled Néel, gapless spin fluid, quantized and partial ferrimagnetic phases. The Haldane phase is limited to the close neighborhood of the isotropic point. Within numerical accuracy, the transition from the gapless spin-fluid phase to the period-doubled Néel phase is a direct transition. Nevertheless, the presence of a narrow spin-gap phase between these two phases is suggested on the basis of the low-energy effective theory. The ferrimagnetic ground state is present in a wide parameter range. This suggests the realization of magnetized single-chain magnets with a uniform spin magnitude by controlling the environment of each magnetic ion without introducing ferromagnetic interactions.
The location of the XY phase in the ground-state phase diagram of the spin-1/2 anisotropic ferromagnetic-antiferromagnetic alternating Heisenberg chain is determined. This model reduces to the spin-1 XXZ chain if the ferromagnetic bond is infinitely strong. The phase boundary between the XY phase and the Haldane phase is determined from the analysis of the numerically obtained energy spectrum of finite-sized systems with the open boundary condition. Our results are consistent with the series-expansion results by Yamanaka et al . within their error bars. The boundary between the ferromagnetic phase and the XY phase is also determined by comparing the energy eigenvalues of these two phases.
Ground state properties, dispersion relations and scaling behaviour of spin gap of a bond alternating spin-1 2 anisotropic Heisenberg chain have been studied where the exchange interactions on alternate bonds are ferromagnetic (FM) and antiferromagnetic (AFM) in two separate cases.The resulting models separately represent nearest neighbour (NN) AFM-AFM and AFM-FM bond alternating chains.Ground state energy has been estimated analytically by using both bond operator and Jordan-Wigner representations and numerically by using exact diagonalization.Dispersion relations, spin gap and several ground state orders have been obtained.Dimer order and string orders are found to coexist in the ground state.Spin gap is found to develop as soon as the non-uniformity in alternating bond strength is introduced in the AFM-AFM chain which further remains non-zero for the AFM-FM chain.This spin gap along with the string orders attribute to the Haldane phase.The Haldane phase is found to exist in most of the anisotropic region similar to the isotropic point.