Symmetrizing the Constraints -- Density Matrix Renormalization Group for Constrained Lattice Models

• URL: http://arxiv.org/abs/2504.04035v3
• Date: Thu, 17 Apr 2025 08:44:37 GMT
• Title: Symmetrizing the Constraints -- Density Matrix Renormalization Group for Constrained Lattice Models
• Authors: Ting-Tung Wang, Xiaoxue Ran, Zi Yang Meng,
• Abstract summary: We develop a density matrix renormalization group (DMRG) algorithm for constrained quantum lattice models.<n>Such an implementation allows us to investigate a quantum dimer model in DMRG for any lattice geometry wrapped around a cylinder with substantial circumference.
• Score: 0.40964539027092917
• License: http://creativecommons.org/licenses/by/4.0/
• 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 $\sqrt{12}\times\sqrt{12}$ 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 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.

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