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

Faster Methods for Contracting Infinite 2D Tensor Networks