  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 $\Gamma$ 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.

Strongly Correlated Electrons