Nuclear norm regularized loop optimization for tensor network

Abstract

We propose a loop optimization algorithm based on nuclear norm regularization for tensor network. The key ingredient of this scheme is to introduce a rank penalty term proposed in the context of data processing. Compared to standard variational periodic matrix product states method, this algorithm can circumvent the local minima related to short-ranged correlation in a simpler fashion. We demonstrate its performance when used as a part of the tensor network renormalization algorithms [S. Yang, Z.-C. Gu, and X.-G. Wen, Phys. Rev. Lett. 118, 110504 (2017)] for the critical 2D Ising model. The scale invariance of the renormalized tensors is attained with higher accuracy while the higher parts of the scaling dimension spectrum are obtained in a more stable fashion.

10 pages, 10 figures

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• Tensor network simulations for nonorientable surfaces
• Finite-size scaling on the torus with periodic projected entangled-pair states
• Tensor Renormalization Group Calculations of Partition-Function Ratios
• Scalable projected entangled-pair state representation of random quantum circuit states
• Tensor renormalization group approach to critical phenomena via symmetry-twisted partition functions
• A Practical Introduction to Tensor Network Renormalization with TNRKit.jl
• Tensor network renormalization approach to antiferromagnetic 6-state clock model on the Union Jack lattice
• Variational boundary based tensor network renormalization group
• Forward-mode automatic differentiation for the tensor renormalization group and its relation to the impurity method
• Lattice and PT symmetries in tensor-network renormalization group: Case study of a hard-square lattice gas model
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