Faster methods for contracting infinite two-dimensional tensor networks

2017/11/30 by M. T. Fishman, Matthew Fishman, Laurens Vanderstraeten +7 · 133 citations
Mathematics · Physics and Astronomy · #Algorithm #Ansatz #Applied mathematics #Combinatorics #Computer science #Density matrix renormalization group #Eigenvalues and eigenvectors #Geometry #Materials science #Mathematical optimization #Mathematical physics #Mathematics #Matrix (chemical analysis) #Matrix multiplication #Matrix product state #Physics #Physics of Superconductivity and Magnetism #Product (mathematics) #Pure mathematics #Quantum #Quantum and electron transport phenomena #Quantum many-body systems #Quantum mechanics #Solver #State (computer science) #Statistical physics #Tensor (intrinsic definition) #Tensor product #Topology (electrical circuits) #Transfer matrix #cond-mat.str-el #quant-ph

paper · pdf · doi:10.1103/physrevb.98.235148

published in Physical review. B./Physical review. B 98(23) (American Physical Society) · 20 pages, 5 figures, V. Zauner-Stauber previously also published under the name V. Zauner

openalex created_date 2017/12/04 · arxiv created 2018/12/02 · openalex publication_date 2018/12/26 · arxiv updated 2019/01/02 · openalex updated_date 2026/08/06

Abstract

We revisit the corner transfer matrix renormalization group (CTMRG) method of Nishino and Okunishi for contracting two-dimensional (2D) tensor networks and demonstrate that its performance can be substantially improved by determining the tensors using an eigenvalue solver as opposed to the power method used in CTMRG. We also generalize the variational uniform matrix product state (VUMPS) ansatz for diagonalizing 1D quantum Hamiltonians to the case of 2D transfer matrices and discuss similarities with the corner methods. These two new algorithms will be crucial to improving the performance of variational infinite projected entangled pair state (PEPS) methods.

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