We study the zero-temperature phase diagram of the J 1 XXZ – J 2 XXZ Heisenberg model for spin-1 particles on an infinite square lattice interacting via nearest-neighbour ( ) and next-nearest-neighbour ( J 2 >0) bonds. The two bonds have the same XXZ -type anisotropy in spin space. The effects on the quasiclassical Néel-ordered and collinear stripe-ordered states of varying the anisotropy parameter Δ are investigated using the coupled cluster method carried out up to high orders. By contrast with the case for spin- particles studied previously, no intermediate disordered phase between the Néel and collinear stripe phases, for any value of the frustration J 2 / J 1 , for either the z -aligned (Δ>1) or xy -planar-aligned (0≤Δ<1) states, is predicted here. The quantum phase transition is determined as first order for all values of J 2 / J 1 and Δ. The position of the phase boundary J 2 c (Δ) is determined accurately. It is observed to deviate most from its classical position (for all values of Δ>0) at the Heisenberg isotropic point (Δ = 1), where J 2 c (1) = 0.55 ± 0.01. By contrast, at the XY isotropic point (Δ = 0), we find J 2 c (0) = 0.50 ± 0.01. In the Ising limit ( ), as expected.
We use a variational mean-field-like approach, the coupled cluster method (CCM), and exact diagonalization to investigate the ground-state order–disorder transition for the square lattice spin-half XXZ model with two different nearest-neighbour couplings J and . On increasing the model shows in the isotropic Heisenberg limit a second-order transition from semi-classical Néel order to a quantum paramagnetic phase with enhanced local dimer correlations on the bonds at about . This transition is driven by the quantum competition between and J . On increasing the anisotropy parameter Δ>1 we diminish the quantum fluctuations and thus the degree of competition. As a result the transition point is shifted to larger values. We find indications for a linear increase of with Δ, i.e. the transition disappears in the Ising limit .
Using the coupled-cluster method for high orders of approximation and Lanczos exact diagonalization we study the ground-state phase diagram of a quantum spin-
21 J1-
J2 model on the square lattice with plaquette structure. We consider antiferromagnetic (
J1>0) as well as ferromagnetic (
J1<0) nearest-neighbor interactions together with frustrating antiferromagnetic next-nearest-neighbor interaction
J2>0. The strength of interplaquette interaction $\ensuremath{\lambda}$ varies between $\ensuremath{\lambda}=1$ (which corresponds to the uniform
J1-
J2 model) and $\ensuremath{\lambda}=0$ (which corresponds to isolated frustrated 4-spin plaquettes). While on the classical level ($s\ensuremath{\rightarrow}\ensuremath{\infty}$) both versions of models (i.e., with ferro- and antiferromagnetic
J1) exhibit the same ground-state behavior, the ground-state phase diagram differs basically for the quantum case
s=1/2. For the antiferromagnetic case (
J1>0) N\'eel antiferromagnetic long-range order at small
J2/J1 and $\ensuremath{\lambda}\ensuremath{\gtrsim}0.47$ as well as collinear striped antiferromagnetic long-range order at large
J2/J1 and $\ensuremath{\lambda}\ensuremath{\gtrsim}0.30$ appear which correspond to their classical counterparts. Both semiclassical magnetic phases are separated by a nonmagnetic quantum paramagnetic phase. The parameter region, where this nonmagnetic phase exists, increases with decreasing $\ensuremath{\lambda}$. For the ferromagnetic case (
J1<0) we have the trivial ferromagnetic ground state at small
J2/∣J1∣. By increasing
J2 this classical phase gives way for a semiclassical plaquette phase, where the plaquette block spins of length
s=2 are antiferromagnetically long-range ordered. Further increasing of
J2 then yields collinear striped antiferromagnetic long-range order for $\ensuremath{\lambda}\ensuremath{\gtrsim}0.38$, but a nonmagnetic quantum paramagnetic phase $\ensuremath{\lambda}\ensuremath{\lesssim}0.38$.
We use cluster mean-field theory, multiple block-product state, and nested cluster methods to study the ground state of a frustrated spin-\textonehalf{} Heisenberg antiferromagnetically stacked square lattice at zero temperature. By analyzing the magnetic order parameter and the geometric measure of entanglement, we find that the stacked model produces a new ordered magnetic phase because of the competition between the interlayer coupling,
Jc, and the frustrated interaction,
J2. The interlayer coupling,
Jc, strengthens the long-range N\'eel phase, the new phase, and the collinear phase and destroys the disordered quantum paramagnetic (QP) phase. Increasing
Jc results in the new phase gradually replacing the QP phase. The QP phase disappears at the critical point
J2∗ = 0.5 and
Jc∗ = 0.12.
We study the effect of spin anisotropies on a frustrated quantum antiferromagnet using the ${J}_{1}\mathrm{\text{\ensuremath{-}}}{J}_{2}^{XXZ}$ model on the square lattice. The
T=0 and finite-
T phase diagrams of this model are obtained utilizing spin-wave theory, exact diagonalization, and quantum Monte Carlo calculations. We find that anisotropic frustration tends to stabilize
XY- and Ising-like ordered phases, while the disordered spin-liquid phase is restricted to a small region of the phase diagram. The ordered phases are separated by first-order transitions and exhibit a nontrivial reentrance phenomenon.
We study the zero-temperature (
T=0) ground-state (GS) properties of a frustrated spin-half
J1XXZ--
J2XXZ model on the honeycomb lattice with nearest-neighbor and next-nearest-neighbor interactions with exchange couplings
J1>0 and ${J}_{2}\ensuremath{\equiv}\ensuremath{\kappa}{J}_{1}>0$, respectively, using the coupled cluster method. Both interactions are of the anisotropic XXZ type. We present the
T=0 GS phase diagram of the model in the ranges $0\ensuremath{\le}\ensuremath{\Delta}\ensuremath{\le}1$ of the spin-space anisotropy parameter and $0\ensuremath{\le}\ensuremath{\kappa}\ensuremath{\le}1$ of the frustration parameter. A possible quantum spin-liquid region is identified.