  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.
