Emergent U(1) Symmetry in Square Lattice Quantum Dimer Models

We report an exact diagonalization study of Rokhsar-Kivelson quantum dimer models on square lattice. Using a finite-size scaling analysis of excited energy levels, we are able to identify a regime of length scales where the the quantum dimer model exhibits a $U(1)$ symmetry. Dimer order parameter histograms confirm this remarkable symmetry. Beyond this crossover length, columnar dimer order emerges at least for $v/t \la 0.6$. Our interpretation is supplemented with field-theory analysis as well as large-scale quantum Monte-Carlo simulations.