Symmetrizing the Constraints -- Density Matrix Renormalization Group for Constrained Lattice Models
arXiv:2504.04035 · doi:10.1103/z4z8-zps4
Abstract
We develop a density matrix renormalization group (DMRG) algorithm for constrained quantum lattice models that successfully {\it{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 triangular lattice, with the symmetry-breaking characteristics of the columnar solid phase and valence bond solid phase fully captured, as well as the topological entanglement entropy of the quantum spin liquid phase that extends to the RK point on non-bipartite lattice accurately revealed. Our DMRG algorithm on constrained quantum lattice models opens new opportunities for matrix and tensor-based algorithms for these systems that have immediate relevance towards the frustrated quantum magnets and synthetic quantum simulators.
12 pages, 8 figures
References in corpus (35)
- The density-matrix renormalization group in the age of matrix product states
- Probing many-body dynamics on a 51-atom quantum simulator
- Probing Topological Spin Liquids on a Programmable Quantum Simulator
- Identifying Topological Order by Entanglement Entropy
- From density-matrix renormalization group to matrix product states
- Tensor network states and algorithms in the presence of a global U(1) symmetry
- Prediction of Toric Code Topological Order from Rydberg Blockade
- Quantum phases of Rydberg atoms on a kagome lattice
- Valence Bond Solids and Their Quantum Melting in Hard-Core Bosons on the Kagome Lattice
- Quantum Many-Body Scar States in Two-Dimensional Rydberg Atom Arrays
- Scaling of entanglement entropy at deconfined quantum criticality
- Measuring Rényi entanglement entropy with high efficiency and precision in quantum Monte Carlo simulations
- Triangular lattice quantum dimer model with variable dimer density
- Quantum Dimer Model on the triangular lattice: Semiclassical and variational approaches to vison dispersion and condensation
- Unifying Kitaev magnets, kagome dimer models and ruby Rydberg spin liquids
- Topological phase transition and single/multi anyon dynamics of spin liquid
- Dynamics of the quantum dimer model on the triangular lattice: Soft modes and local resonating valence-bond correlations
- Identification of an RVB liquid phase in a quantum dimer model with competing kinetic terms
- Topological Disorder Parameter
- Quantum Electrodynamics in 2+1 Dimensions as the Organizing Principle of a Triangular Lattice Antiferromagnet
- Crystallization of the resonating valence bond liquid as vortex condensation
- Fractionalized conductivity and emergent self-duality near topological phase transitions
- Double Semion Phase in an Exactly Solvable Quantum Dimer Model on the Kagome Lattice
- Extracting subleading corrections in entanglement entropy at quantum phase transitions
- Evolution of entanglement entropy at SU() deconfined quantum critical points
- String Picture of a Frustrated Quantum Magnet and Dimer Model
- Quantum dimer models with Rydberg gadgets
- Entanglement Entropy at Generalized Rokhsar-Kivelson Points of Quantum Dimer Models
- Stability of scar states in 2D PXP model against random disorders
- An analog of topological entanglement entropy for mixed states
- Unconventional Scalings of Quantum Entropies in Long-Range Heisenberg Chains
- Hidden orders and phase transitions for the fully packed quantum loop model on the triangular lattice
- Extracting Universal Corner Entanglement Entropy during the Quantum Monte Carlo Simulation
- Cubic* criticality emerging from a quantum loop model on triangular lattice
- Vison condensation and spinon confinement in a kagome-lattice spin liquid: A numerical study of a quantum dimer model