Global optimization of tensor renormalization group using the corner transfer matrix

Abstract

A tensor network renormalization algorithm with global optimization based on the corner transfer matrix is proposed. Since the environment is updated by the corner transfer matrix renormalization group method, the forward-backward iteration is unnecessary, which is a time-consuming part of other methods with global optimization. In addition, a further approximation reducing the order of the computational cost of contraction for the calculation of the coarse-grained tensor is proposed. The computational time of our algorithm in two dimensions scales as the sixth power of the bond dimension while the higher-order tensor renormalization group and the higher-order second renormalization group methods have the seventh power. We perform benchmark calculations in the Ising model on the square lattice and show that the time-to-solution of the proposed algorithm is faster than that of other methods.

6 pages, 9 figures

References in corpus (2)

• Tensor renormalization group approach to 2D classical lattice models
• Entanglement branching operator

Cited by in corpus (9)

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• Scaling dimensions from linearized tensor renormalization group transformations
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• Triad second renormalization group
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• Multi-impurity method for the bond-weighted tensor renormalization group
• All-mode Renormalization for Tensor Network with Stochastic Noise
• Forward-mode automatic differentiation for the tensor renormalization group and its relation to the impurity method
• Variational boundary based tensor network renormalization group