A theoretical model is presented to explain the spin gap observed for
CaV4O9. The underlying lattice of the 1/5-depleted square lattice favors a formation of the plaquette resonating-valence-bond state. Inclusion of the frustrating second neighbor interaction enhances this tendency, leading to a quantum disordered state of a two-dimensional spin-1/2 Heisenberg model with a sufficiently big spin gap compatible with experiments.
We examine the ground state and the excitations of an one-dimensional Heisenberg spin 1/2 antiferromagnet with alternating dimers and four-spin plaquettes (dimer-plaquette chain). The properties of the system depend on the competing dimer and plaquette bonds. Several exact, exact-numerical and perturbational results are presented. We find that the system is gapped for all parameter values. For the latter one we find an effective S=1 Haldane like behaviour in the limit of dominating dimer bonds. The model considered is related to the recently found 1/5-depleted square-lattice Heisenberg system
CaV4O9.
We revisit the SU(6) Heisenberg model on the honeycomb lattice, which has been predicted to be a chiral spin liquid by mean-field theory [G. Szirmai et al., Phys. Rev. A 84, 011611(R) (2011)]. Using exact diagonalizations of finite clusters, infinite projected entangled pair state simulations, and variational Monte Carlo simulations based on Gutzwiller projected wave functions, we provide strong evidence that the model with one particle per site and nearest-neighbor exchange actually develops plaquette order. This is further confirmed by the investigation of the model with a ring-exchange term, which shows that there is a transition between the plaquette state and the chiral state at a finite value of the ring-exchange term.
We study the half-filled single-band Hubbard model on the Shastry–Sutherland lattice with nearest-neighbor hopping
t, incorporating (i) a frustrating diagonal hopping
t′ to probe the emergence of spin-liquid behavior, and (ii) an additional Heisenberg exchange
J that explicitly stabilizes plaquette-singlet correlations. Using the variational cluster approximation (VCA) with exact diagonalization at zero temperature on an eight-site cluster, we map the phase diagrams in the
(U/t,t′/t) and
(U/t,J/t) parameter planes. In the
(U/t,t′/t) plane, our analysis uncovers a competition between N\'eel antiferromagnetic (AFM) order with staggered magnetization and a nonmagnetic regime lacking conventional order, consistent with an algebraic spin-liquid (ASL) phase characterized by a gapped excitation spectrum and vanishing staggered magnetization. In contrast, the
(U/t,J/t) phase diagram exhibits a competition between the N\'eel AFM and a solid valence-bonding valence bond plaquette (PS), where spins form localized singlet plaquettes. Most notably, we observe that the transition from the PS phase to the N\'eel AFM is a first-order phase transition, with a discontinuous jump of the order parameters at the phase boundary, in quantitative agreement with high-pressure heat-capacity measurements on SrCu
2(BO
3)
2 [Guo \emph{et al.}, Commun. Phys. 8, 75 (2025)]. Thus, our VCA analysis underscores the subtle interplay of geometric frustration, quantum fluctuations, and dimensionality, and elucidates the crucial role of short-range correlations in stabilizing and competing ground states of frustrated quantum magnets.
We investigate the mechanism of spin gap formation in a two-dimensional model relevant to Mott insulators such as CaV
4O
9. From the perturbation expansion and quantum Monte Carlo calculations, the origin of the spin gap is ascribed to the four-site plaquette singlet in contrast to the dimer gap established in the generalized dimerized Heisenberg model.