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

Abstract

<p>We develop a density matrix renormalization group (DMRG) algorithm for constrained quantum lattice models that successfully <em>implements the local constraints as symmetries in the contraction of the matrix product states and matrix product operators</em>. 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 √12×√12 valence bond solid phase fully captured, as well as the topological entanglement entropy of the ℤ2 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.</p>