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Plaquette valence-bond solid in the square lattice J1-J2 antiferromagnet Heisenberg model: a bond operator approach

We study the plaquette valence-bond solid phase of the spin-1/2 J_1-J_2 antiferromagnet Heisenberg model on the square lattice within the bond-operator theory. We start by considering four S = 1/2 spins on a single plaquette and determine the bond operator representation for the spin operators in terms of singlet, triplet, and quintet boson operators. The formalism is then applied to the J_1-J_2 model and an effective interacting boson model in terms of singlets and triplets is derived. The effective model is analyzed within the harmonic approximation and the previous results of Zhitomirsky and Ueda [Phys. Rev. B 54, 9007 (1996)] are recovered. By perturbatively including cubic (triplet-triplet-triplet and singlet-triplet-triplet) and quartic interactions, we find that the plaquette valence-bond solid phase is stable within the parameter region 0.34 < J_2/J_1 < 0.59, which is narrower than the harmonic one. Differently from the harmonic approximation, the excitation gap vanishes at both critical couplings J_2 = 0.34 J_1 and J_2 = 0.59 J_1. Interestingly, for J_2 < 0.48 J_1, the excitation gap corresponds to a singlet-triplet excitation at the $Γ$ point while, for J_2 > 0.48 J_1, it is related to a singlet-singlet excitation at the X = (pi/2,0) point of the tetramerized Brillouin zone.