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DMRG Approach to Optimizing Two-Dimensional Tensor Networks

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arxiv 1908.08833 v2 pith:FO6D4B2V submitted 2019-08-23 cond-mat.str-el quant-ph

Katharine Hyatt , E. M. Stoudenmire This is my paper · ORCID
classification cond-mat.str-elquant-ph
keywords tensornetworksoptimizingdmrgtwo-dimensionalalgorithmsknownmake
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Tensor network algorithms have been remarkably successful solving a variety of problems in quantum many-body physics. However, algorithms to optimize two-dimensional tensor networks known as PEPS lack many of the aspects that make the seminal density matrix renormalization group (DMRG) algorithm so powerful for optimizing one-dimensional tensor networks known as matrix product states. We implement a framework for optimizing two-dimensional PEPS tensor networks which includes all of steps that make DMRG so successful for optimizing one-dimension tensor networks. We present results for several 2D spin models and discuss possible extensions and applications.

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Cited by 3 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Diagonal Isometric Form for Tensor Network States in Two Dimensions

    cond-mat.str-el 2025-07 conditional novelty 7.0 of 10

    A new isometric form for 2D tensor network states uses auxiliary tensors on a 45-degree rotated lattice, enabling a local Yang-Baxter move and a TEBD algorithm that captures area-law ground states and short-time dynamics.

  2. Pauli propagation enables fast classical simulation of strongly correlated quantum systems

    quant-ph 2025-11 conditional novelty 6.0 of 10

    A classical algorithm combining sparse Pauli dynamics with a variational double bracket flow estimates ground-state energies of Heisenberg and Hubbard models with sub-1% error vs DMRG, with large speedups on some 2D systems.

  3. Advantages of density in tensor network geometries for gradient based training

    quant-ph 2024-12 conditional novelty 6.0 of 10

    Densely connected tensor network geometries train to lower infidelity than sparse ones on random quantum states, and a new leaf-contraction trick reduces memory while improving training.

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