We study a spin chain and a three-dimensional spin lattice with ground states given by a product of spin-singlet nearest-neighbor pairs. In a magnetic field, the ground state and low-lying states are a mixture of spin singlets and spin-polarized triplets; these states are highly degenerate. When the lattice is distorted, hopping terms are introduced which lift the degeneracy. For particular parameter ranges, the magnetization versus magnetic-field curve exhibits spin plateaus, when the excited states are separated from the ground state by a spin gap. At a critical point, the plateau and the corresponding gap vanish. This spin system is embedded in a more general interacting electron system, and when doped, the charged carriers are found to bind in pairs.
We construct a class of spin-1/2 antiferromagnetic two-chain ladder models consisting of blocks of n-spin tetrahedral clusters alternating with two-spin rungs. For
n=4 and 6 and in extended parameter regimes, the exact ground state of the ladder is shown to be a product of the ground states of the rungs and the n-spin blocks, in both zero and finite magnetic fields. In the latter case, magnetization/site m versus magenetic field h plot exhibits well-defined magnetization plateaus.
We study magnetic excitations for anisotropic spin dimer systems. We present a theory that describes not only the lowest-lying excitation mode but also higher-lying modes of the spin dimers, where the latter modes are important for quantum phase transitions driven by magnetic field and pressure in spin-gapped systems. As the most intriguing application, we calculate electron spin resonance (ESR) intensity in the presence of Dzyaloshinskii–Moriya (DM) interaction, which couples the local triplet with the singlet states of the dimer. The ESR intensities under various configurations of the DM interactions are reported in both disordered and field-induced ordered phases, which are very useful for the analysis of high-field ESR data.
The ground state and zero-temperature magnetization process of the spin-1/2 Ising-Heisenberg model on two-dimensional triangles-in-triangles lattices are exactly calculated using eigenstates of the smallest commuting spin clusters. Our ground-state analysis of the investigated classical-quantum spin model reveals three unconventional dimerized or trimerized quantum ground states besides two classical ground states. It is demonstrated that the spin frustration is responsible for a variety of magnetization scenarios with up to three or four intermediate magnetization plateaus of either quantum or classical nature. The exact analytical results for the Ising-Heisenberg model are confronted with the corresponding results for the purely quantum Heisenberg model, which were obtained by numerical exact diagonalizations based on the Lanczos algorithm for finite-size spin clusters of 24 and 21 sites, respectively. It is shown that the zero-temperature magnetization process of both models is quite reminiscent, and hence, one may obtain some insight into the ground states of the quantum Heisenberg model from the rigorous results for the Ising-Heisenberg model even though exact ground states for the Ising-Heisenberg model do not represent true ground states for the pure quantum Heisenberg model.
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.