Symmetrizing the constraints: Density matrix renormalization group for constrained lattice models

We develop a density matrix renormalization group (DMRG) algorithm for constrained quantum lattice models that successfully implements the local constraints as symmetries in the contraction of the matrix product states and matrix product operators. Such an implementation allows us to investigate a quantum dimer model in DMRG for any lattice geometry wrapped around a cylinder with substantial circumference. We have thence computed the ground-state phase diagram of the quantum dimer model on a triangular lattice, with the symmetry-breaking characteristics of the columnar solid phase and $\sqrt{12}\ifmmode\times\else\texttimes\fi{}\sqrt{12}$ valence bond solid phase fully captured, as well as the topological entanglement entropy of the ${\mathbb{Z}}_{2}$ quantum spin-liquid phase that extends to the Rokhsar-Kivelson point on nonbipartite lattice accurately revealed. Our DMRG algorithm opens new opportunities for tensor-based approaches to constrained models, including but not limited to dimer-type systems. Such models are often directly relevant to frustrated quantum magnets and synthetic quantum simulators.