By means of the recently proposed algorithm based on the tensor product states, the magnetization process of the spin-1/2 antiferromagnetic XXZ model on a square lattice is investigated. In the large spin-anisotropy limit, clear evidence of a first-order spin–flip transition is observed as an external magnetic field is increased. Our findings of the critical field and the discrete jumps in various local order parameters are in good agreement with the quantum Monte Carlo data in the literature. Our results imply that this algorithm can be an accurate and efficient numerical approach in studying first-order quantum phase transitions in two dimensions.
The phase diagrams of Ising antiferromagnets in a magnetic field
H are investigated for various values of the ratio
R between nearest- and next-nearest-neighbor interaction. While meanfield approximations and the existing real-space renormalization-group treatments yield phase diagrams which are sometimes even qualitatively incorrect, accurate results are obtained from Monte Carlo calculations. For
R<0 only an antiferromagnetically ordered phase exists. Its transition to the disordered phase is first order for temperatures below the tricritical point (
Tt,
Ht). For $R\ensuremath{\rightarrow}0$ also ${T}_{t}\ensuremath{\rightarrow}0$. For
R=0 we find very good agreement with the results of M\"uller-Hartmann and Zittartz. For
R>0 and
H1<H<H2 a new phase with anomalous high ground-state degeneracy is found (two sublattices have only one-dimensional order). These sublattices undergo order-disorder transitions at
T=0, such that for
T>0 one is left with a "superantiferromagnetic" phase. At low temperatures in this phase a pronounced tendency is observed to form a simpler (2 \ifmmode\times\else\texttimes\fi{} 2) superstructure but with many antiphase domain boundaries. For $R\ensuremath{\rightarrow}\frac{1}{2}$ and
H<H1 the regime of the antiferromagnetic phases goes to zero temperature, while for
R>21 the superantiferromagnetic phase exists also for
H<H1. The order-disorder transition associated with this phase seems to have non-Ising critical exponents which vary as a function of
R and
H. Estimates for the exponents lead us to suggest that Suzuki's "weak universality" is valid. The behavior of the model at
T=0 is related to known results on hard-core lattice gases. It is shown that it is useful to interpret the transitions at
T=0 as generalized percolation transitions. Since the model may have applications to adsorbate phases in registered structures at (100) surfaces of cubic crystals, the transcription of our results to temperature-coverage phase diagrams and adsorption isotherms is discussed in detail, and possible experimental applications are mentioned.
Plateaux in the magnetization curves of the square-, triangular- and hexagonal-lattice spin-1/2 XXZ antiferromagnet are investigated. One finds a zero-magnetization plateau (corresponding to a spin gap) on the square and hexagonal lattice with Ising-like anisotropies, and a plateau with one-third of the saturation magnetization on the triangular lattice which survives a small amount of easy-plane anisotropy. Here we start with transfer-matrix computations for the Ising limit and continue with series in the XXZ anisotropy for plateau boundaries using the ground states of the Ising limit. The main focus is then a numerical computation of the magnetization curves with anisotropies in the vicinity of the isotropic situation. Finally, we discuss the universality class associated with the asymptotic behaviour of the magnetization curve close to saturation, as observed numerically in two and higher dimensions.
We determine the zero-temperature phase diagram of the hard-core Bose-Hubbard model on a square lattice by mean-field theory supplemented by a linear spin-wave analysis. Due to the interplay between nearest- and next-nearest-neighbor interaction and cubic anisotropy several supersolid phases with checkerboard, stripe-domain, or intermediate symmetry are stabilized. The phase diagrams show three different topologies depending on the relative strength of nearest- and next-nearest-neighbor interaction. We also find a rich variety of new quantum critical behavior and multicritical points and discuss the corresponding effective actions and universality classes.
Using quantum Monte Carlo (QMC) simulations and a mean field theory, we investigate the spin-1/2
XXZ model with nearest-neighbor interactions on a periodic depleted square lattice. In particular, we present results for 1/4 depleted lattice in an applied magnetic field and investigate the effect of depletion on the ground state. The ground state phase diagram is found to include an antiferromagnetic (AF) phase of magnetization ${m}_{z}=\ifmmode\pm\else\textpm\fi{}1/6$ and an in-plane ferromagnetic (FM) phase with finite spin stiffness. The agreement between the QMC simulations and the mean-field theory based on resonating trimers suggests the AF phase and in-plane FM phase can be interpreted as a Mott insulator and superfluid of trimer states, respectively. While the thermal transitions of the in-plane FM phase are well described by the Kosterlitz-Thouless transition, the quantum-phase transition from the AF phase to in-plane FM phase undergo a direct second-order insulator-superfluid transition upon increasing magnetic field.
The transverse high-spin Ising model with different single-ion anisotropies is studied in the ground state within the mean-field theory and the correlated effective-field theory.The expressions of magnetization and energy in the finite temperature and ground state are derived and the results are got numerically.The ground-state phase diagram is obtained within the mean-field theory,and the ground-state phase diagrams for the honeycomb lattice,the square lattice and the simple cubic lattice are gained,respectively,within the correlated effective theory.The focus of this paper is on the difference of phase transition properties within the mean-field theory and the correlated effective-field theory.