  The quantum dimer and loop models attract great attentions, partially because
the fundamental importance in the phases and phase transitions emerging in
these prototypical constrained systems, and partially due to their intimate
relevance toward the on-going experiments on Rydberg atom arrays in which the
blockade mechanism naturally enforces the local constraint. Here we show, by
means of the sweeping cluster quantum Monte Carlo method, the complete ground
state phase diagram of the fully packed quantum loop model on the square
lattice. We find between the lattice nematic (LN) phase with strong dimer
attraction and the staggered phase (SP) with strong dimer repulsion, there
emerges a resonating plaquette (RP) phase with off-diagonal translational
symmetry breaking. Such a quantum phase is separated from the LN via a first
order transition and from the SP by the famous Rokhsar-Kivelson point. Our
renormalization group analysis reveals the different flow directions, fully
consistent with the order parameter histogram in Monte Carlo simulations. The
realization and implication of our phase diagram in Rydberg experiments are
proposed.
