In this study, an order by disorder mechanism has been proposed in a two-dimensional PXP model, where the extensive degeneracy of the classical ground-state manifold is due to strict occupation constraints instead of geometrical frustrations. By performing an unbias large-scale quantum monte carlos simulation, we find that local quantum fluctuations, which usually work against long-range ordering, lift the macroscopic classical degeneracy and give rise to a compressible ground state with charge-density-wave long-range order. A simple trial wavefunction has been proposed to capture the essence of the ground-state of the two-dimensional PXP model. The finite temperature properties of this model have also been studied, and we find a thermal phase transition with an universality class of two-dimensional Ising model.
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