We investigate the
S=2 antiferromagnetic quantum spin chain with the exchange and single-ion anisotropies in a magnetic field, using the numerical exact diagonalization of finite-size clusters and the level spectroscopy analysis. It is found that a magnetization plateau possibly appears at half of the saturation magnetization for some suitable anisotropy parameters. The level spectroscopy analysis indicates that the 1/2 magnetization plateau is formed by two different mechanisms, depending on the anisotropy parameters. The phase diagram of the 1/2 plateau states and some typical magnetization curves are also presented. In addition, the biquadratic interaction is revealed to enhance the plateau induced by the Haldane mechanism.
The magnetization process of the one-dimensional antiferromagnetic Heisenberg model with the Ising-like anisotropic exchange interaction is studied by the exact diagonalization technique. It results in the evidence of the first-order spin-flop transition with a finite magnetization jump in the N\'eel ordered phase for
S> 1. It implies that the
S=21 chain is an exceptional case where the metamagnetic transition becomes second order due to large quantum fluctuations.
We generalize a class of Heisenberg antiferromagnets in one, two, and three dimensions, which have been shown to exhibit magnetization plateaus for spin-
21. In a certain parameter range of the general model, which is formally defined in
D dimensions, we obtain the exact ground state(s) in the presence of an external magnetic field for arbitrary values of spin. In this range, the magnetization remains a constant as a function of the external field, except at some special values of the field where there is a jump from one plateau to the next. The plateaus are formed at certain specific fractions of the full magnetization which are determined by the spin and the lattice. Our general spin-
S result reproduces the known cases for spin-
21 in various lattices. Furthermore, we argue that outside the exact regime, the mechanism for the plateau formation is different. This results in first order phase transitions along some of the plateaus as the coupling constant is varied. We rigorously show the existence of such transitions for some particular cases. Finally, we numerically analyze a spin-
1 model in one dimension using exact diagonalization to obtain its complete phase diagram. It agrees with our analytic results.
The ground state of the spin-1/2 Ising–Heisenberg distorted diamond chain in the presence of an external magnetic field is investigated in the case of the ferromagnetic Ising and antiferromagnetic XXZ Heisenberg interactions, that exhibits a geometric frustration of spins. The influence of the quantum fluctuations, the magnetic field, and the distortion on the ground state are studied in detail. It is established that the zero-temperature magnetization curve may show intermediate plateaus at zero and one-third of the saturation magnetization.
We study the magnetization process of a one-dimensional extended Heisenberg model, the $J\text{\ensuremath{-}}Q$ model, as a function of an external magnetic field
h. In this model,
J represents the traditional antiferromagnetic Heisenberg exchange and
Q is the strength of a competing four-spin interaction. Without external field, this system hosts a twofold-degenerate dimerized (valence-bond solid) state above a critical value ${q}_{c}\ensuremath{\approx}0.85$ where $q\ensuremath{\equiv}Q/J$. The dimer order is destroyed and replaced by a partially polarized translationally invariant state at a critical field value. We find magnetization jumps (metamagnetism) between the partially polarized and fully polarized state for
q>qmin, where we have calculated
qmin=92 exactly. For
q>qmin, two magnons (flipped spins on a fully polarized background) attract and form a bound state. Quantum Monte Carlo studies confirm that the bound state corresponds to the first step of an instability leading to a finite magnetization jump for
q>qmin. Our results show that neither geometric frustration nor spin anisotropy are necessary conditions for metamagnetism. Working in the two-magnon subspace, we also find evidence pointing to the existence of metamagnetism in the unfrustrated ${J}_{1}\text{\ensuremath{-}}{J}_{2}$ chain
(J1>0,J2<0), but only if
J2 is spin anisotropic. In addition to the studies at zero temperature, we also investigate quantum-critical scaling near the transition into the fully polarized state for $q\ensuremath{\le}{q}_{\mathrm{min}}$ at
T>0. While the expected ``zero-scale-factor'' universality is clearly seen for
q=0 and $q\ensuremath{\ll}{q}_{\mathrm{min}}$, for
q closer to
qmin we find that extremely low temperatures are required to observe the asymptotic behavior, due to the influence of the tricritical point at
qmin. In the low-energy theory, one can expect the quartic nonlinearity to vanish at
qmin and a marginal sixth-order term should govern the scaling, which leads to a crossover at a temperature
T∗(q) between logarithmic tricritical scaling and zero-scale-factor universality, with ${T}^{*}(q)\ensuremath{\rightarrow}0$ when $q\ensuremath{\rightarrow}{q}_{\mathrm{min}}$.
The exactly solvable spin-1/2 Ising-Heisenberg distorted diamond chain in the presence of the external magnetic field is investigated for the case of antiferromagnetic Ising and ferromagnetic XXZ Heisenberg interactions. The influence of quantum fluctuations and the distortion on the ground state, magnetic and thermal properties of the model are studied in detail.In particular, it is established that the zero-temperature magnetization curve may involve intermediate plateaus just at zero and 1/3 of the saturation magnetization. It is demonstrated that the temperature dependence of the specific heat reveals up to four distinct peaks at zero magnetic field and up to five distinct peaks at a weak magnetic field. The physical origin of all observed additional peaks of the specific heat has been clarified on the grounds of dominating thermal excitations. We have shown that the quantum fluctuations give rise to an effective geometrical frustration in this chain.