Applying Bohr-Sommerfeld quantization and the topological phase of spin path integrals, one can determine the multiplicities, lattice symmetries, and eigenvalue clustering pattern of the low-lying singlet eigenstates of the triangular and fcc antiferromagnets with four-sublattice classical ground states. In the triangular case, the clustering pattern agrees with numerical results of Lecheminant et al. [Phys. Rev. B 52, 6647 (1995)].
'Resonating-valence-bond' (RVB) variational wavefunctions are numerically investigated in order to describe the ground state and the singlet low-lying excited states of the spin-1/2, J 1 -J 2 Heisenberg antiferromagnet with 1/8<or approximately=J 2 /J 1 <or approximately=1 on triangular lattices of N=4p sites compatible with the classical Neel orders. Comparison with previous exact diagonalization results indicates that the singlet eigenstates associated with collinear Neel order, among which the ground state is found, can be accurately described with appropriate superpositions of two-sublattice RVB trial states, while the other singlet low-lying eigenstates associated with four-sublattice Neel order can be well approximated from the four-sublattice RVB trial states.
We study the low-lying eigenenergy clustering patterns of quantum antiferromagnets with p sublattices (in particular
p=4). We treat each sublattice as a large spin, and using second-order degenerate perturbation theory, we derive the effective (biquadratic) Hamiltonian coupling the p large spins. In order to compare with exact diagonalizations, the Hamiltonian is explicitly written for a finite-size lattice, and it contains information on energies of excited states as well as the ground state. The result is applied to the face-centered-cubic Type-I antiferromagnet of spin 1/2, including second-neighbor interactions. A 32-site system is exactly diagonalized, and the energy spectrum of the low-lying singlets follows the analytically predicted clustering pattern.
Quantum magnetic phases near the magnetic saturation of triangular-lattice antiferromagnets with XXZ anisotropy have been attracting renewed interest since it has been suggested that a nontrivial coplanar phase, called the $\ensuremath{\pi}$-coplanar or $\mathrm{\ensuremath{\Psi}}$ phase, could be stabilized by quantum effects in a certain range of anisotropy parameter
J/Jz besides the well-known 0-coplanar (known also as
V) and umbrella phases. Recently, Sellmann et al. [Phys. Rev. B 91, 081104(R) (2015)] claimed that the $\ensuremath{\pi}$-coplanar phase is absent for
S=1/2 from an exact-diagonalization analysis in the sector of the Hilbert space with only three down-spins (three magnons). We first reconsider and improve this analysis by taking into account several low-lying eigenvalues and the associated eigenstates as a function of
J/Jz and by sensibly increasing the system sizes (up to 1296 spins). A careful identification analysis shows that the lowest eigenstate is a chirally antisymmetric combination of finite-size umbrella states for $J/{J}_{z}\ensuremath{\gtrsim}2.218$ while it corresponds to a coplanar phase for $J/{J}_{z}\ensuremath{\lesssim}2.218$. However, we demonstrate that the distinction between 0-coplanar and $\ensuremath{\pi}$-coplanar phases in the latter region is fundamentally impossible from the symmetry-preserving finite-size calculations with fixed magnon number. Therefore, we also perform a cluster mean-field plus scaling analysis for small spins $S\ensuremath{\le}3/2$. The obtained results, together with the previous large-
S analysis, indicate that the $\ensuremath{\pi}$-coplanar phase exists for any
S except for the classical limit $(S\ensuremath{\rightarrow}\ensuremath{\infty})$ and the existence range in
J/Jz is largest in the most quantum case of
S=1/2.