Real-Space Parallel Density Matrix Renormalization Group

Abstract

We demonstrate how to parallelize the density matrix renormalization group (DMRG) algorithm in real space through a straightforward modification of serial DMRG. This makes it possible to apply at least an order of magnitude more computational power to challenging simulations, greatly accelerating investigations of two-dimensional systems and large parameter spaces. We discuss details of the algorithm and present benchmark results including a study of valence-bond-solid order within the square-lattice Q2 model and Neel order within the triangular lattice Heisenberg model. The parallel DMRG algorithm also motivates an alternative canonical form for matrix product states.

5 pages, 5 figures; New version includes triangular Heisenberg AFM, discussion of inverse MPS gauge, and accurate SVD algorithm (similar to PRB version)

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• Generic Construction of Efficient Matrix Product Operators
• Isometric Tensor Network States in Two Dimensions
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• Automatic structural optimization of tree tensor networks
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• Nature of quantum spin liquids of the S=1/2 Heisenberg antiferromagnet on the triangular lattice: A parallel DMRG study
• Tensor Networks for Lattice Gauge Theories beyond one dimension: a Roadmap
• Quantum-inspired event reconstruction with Tensor Networks: Matrix Product States
• Absence of Luther-Emery Superconducting Phase in the Three-Band Model for Cuprate Ladders
• Monte Carlo simulations of two-dimensional fermion systems with string-bond states
• Distributed-Memory DMRG via Sparse and Dense Parallel Tensor Contractions
• Performance of the rigorous renormalization group for first order phase transitions and topological phases
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• Emergent Quantum Mechanics at the Boundary of a Local Classical Lattice Model
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• Absence of superconductivity in the Hubbard dimer model for kappa-(BEDT-TTF)_2X
• Density Matrix Renormalization Group study of superconducting pairing near the quarter-filled Wigner crystal
• The Software Landscape for the Density Matrix Renormalization Group
• Build your own tensor network library: DMRjulia I. Basic library for the density matrix renormalization group
• High-precision ground state parameters of the two-dimensional spin-1/2 Heisenberg model on the square lattice
• Fractal Path Strategies for Efficient 2D DMRG Simulations