We develop a systematic large-
N expansion based on the Schwinger boson representation of SU(4) coherent states of dimers for the paradigmatic spin-
1/2 bilayer square lattice Heisenberg antiferromagnet. This system exhibits a quantum phase transition between a quantum paramagnetic state and a Néel order state, driven by the coupling constant
g=J′/J, which is defined as the ratio between the inter-dimer
J′ and intra-dimer
J exchange interactions. We demonstrate that this approach accurately describes static and dynamic properties on both sides of the quantum phase transition. The critical coupling constant
gc≈0.42 and the dynamic spin structure factor reproduce quantum Monte Carlo results with high precision. Notably, the
1/N corrections reveal the longitudinal mode of the magnetically ordered phase along with the overdamping caused by its decay into the two-magnon continuum. The present large-
N SU(N) Schwinger boson theory can be extended to more general cases of quantum paramagnets that undergo a quantum phase transition into magnetically ordered states.
A generalized Schwinger boson representation is proposed to describe the two-dimensional SU(4) symmetric spin-orbital quantum antiferromagnet. A uniform mean field solution gives rise to an antiferromagnetic long range ordered state with a small staggered magnetization
ms=0.07566, and the recent quantum Monte Carlo simulations on rather large lattice sizes have provided strong evidence to support these mean field results.