The magnetization curve of the two-dimensional spin-1/2 ${J}_{1}\ensuremath{-}{J}_{2}$ Heisenberg model is investigated by using the Chern-Simons theory under mean-field approximations. We find that the magnetization curve increases monotonically for
J2/J1<0.267949, where the system under zero external field is in the antiferromagnetic N\'eel phase. For larger ratios of
J2/J1, various plateaus will appear in the magnetization curve. In particular, in the disordered phase, our results support the existence of the
M/Msat=1/2 plateau, and predict a plateau at
M/Msat=1/3. Verification of these interesting results would indicate a strong connection between the frustrated antiferromagnetic system and the quantum Hall system.
The dynamical spin structure factor is computed within a variational framework to study the one-dimensional ${J}_{1}\ensuremath{-}{J}_{2}$ Heisenberg model. Starting from Gutzwiller-projected fermionic wave functions, the low-energy spectrum is constructed from two-spinon excitations. The direct comparison with Lanczos calculations on small clusters demonstrates the excellent description of both gapless and gapped (dimerized) phases, including incommensurate structures for
J2/J1>0.5. Calculations on large clusters show how the intensity evolves when increasing the frustrating ratio and give an unprecedented accurate characterization of the dynamical properties of (nonintegrable) frustrated spin models.
We report on recent results for strongly frustrated quantum J1 - J2 antiferromagnets in dimensionality d = 1, 2, 3 obtained by the coupled cluster method (CCM). We demonstrate that the CCM in high orders of approximation allows us to investigate quantum phase transitions driven by frustration and to discuss novel quantum ground states. In detail we consider the ground-state properties of (i) the Heisenberg spin-1/2 antiferromagnet on the cubic lattice in d = 1, 2, 3, and use the results for the energy, the sublattice magnetization and the spin stiffness as a benchmark test for the precision of the method; (ii) coupled frustrated spin chains (the quasi-one-dimensional J1 - J2 model) and discuss the influence of the quantum fluctuations and the interchain coupling on the incommensurate spiral state present in the classical model; (iii) the Shastry-Sutherland antiferromagnet on the square lattice; and (iv) a stacked frustrated square-lattice Heisenberg antiferromagnet (the quasi-two-dimensional J1 - J2 model), and discuss the influence of the interlayer coupling on the quantum paramagnetic ground-state phase that is present for the strictly two-dimensional model.