It is well known that the ground state of low-dimensional antiferromagnets deviates from Neel states due to strong quantum fluctuations. Even in the presence of long-range order, those fluctuations produce a substantial reduction of the magnetic moment from its saturation value. Numerical simulations in anisotropic antiferromagnetic chains suggest that quantum fluctuations over Neel order appear in the form of localized reversal of pairs of neighboring spins. In this paper, we propose a coherent state representation for the ground state to describe the above situation. In the one-dimensional case, our wave function corresponds to a two-mode Glauber state, when the Neel state is used as a reference, while the boson fields are associated to coherent flip of spin pairs. The coherence manifests itself through the antiferromagnetic long-range order that survives the action of quantum fluctuations. The present representation is different from the standard zero-point spin wave state, and is asymptotically exact in the limit of strong anisotropy. The fermionic version of the theory, obtained through the Jordan-Wigner transformation, is also investigated.
I define a set of wave functions for
SU(N) lattice antiferromagnets, analogous to the valence bond solid states of Affleck et al. [Phys. Rev. Lett. 59, 799 (1987); Commun. Math. Phys. 115, 477 (1988)], in which the singlets are extended over
N-site simplixes. As with the valence bond solids, the new simplex solid (SS) states are extinguished by certain local projection operators, allowing one to construct Hamiltonians with local interactions which render the SS states exact ground states. Using a coherent state representation, I show that the quantum correlations in each SS state are calculable as the finite temperature correlations of an associated classical model with
N-spin interactions on the same lattice. In three and higher dimensions, the SS states can spontaneously break
SU(N) and exhibit
N-sublattice long-ranged order as a function of a discrete parameter which fixes the local representation of
SU(N). I analyze this transition using a classical mean field approach. For
N>2, the ordered state is selected via an ``order by disorder'' mechanism. As in the Affleck-Kennedy-Lieb-Tasaki case, the bulk representations fractionalize at an edge, and the ground state entropy is proportional to the volume of the boundary.
Abstract. We study the structure of quantum ground states of simplex solid models, which are generalizations of the valence bond construction for quantum antiferromagnets originally proposed by Affleck, Kennedy, Lieb, and Tasaki (AKLT) (1987 Phys. Rev. Lett . 59 799). Whereas the AKLT states are created by application of bond singlet operators for spins, the simplex solid construction is based on N -simplex singlet operators for spins. In both cases, a discrete one-parameter family of translationally-invariant models with exactly solvable ground states is defined on any regular lattice, and the equal time ground state correlations are given by the finite temperature correlations of an associated classical model on the same lattice, owing to the product form of the wave functions when expressed in a coherent state representation. We study these classical companion models via a mix of Monte Carlo simulations, mean-field arguments, and low-temperature effective field theories. Our analysis reveals that the ground states of edge- and face-sharing cubic lattice simplex solid models are long range ordered for sufficiently large values of the discrete parameter, whereas the ground states of the models on the kagome (2D) and hyperkagome (3D) lattices are always quantum disordered. The kagome simplex solid exhibits strong local order absent in its three-dimensional hyperkagome counterpart, a contrast that we rationalize with arguments similar to those leading to ‘order by disorder’.