Applying the Triad network representation to four-dimensional ATRG method

Abstract

Anisotropic Tensor Renormalization Group (ATRG) is a powerful algorithm for four-dimensional tensor network calculations. However, the larger bond dimensions are known to be difficult to achieve in practice due to the higher computational cost. Adopting the methods of the minimally decomposed TRG and its triad prescriptions, we construct a triad representation of the four-dimensional ATRG by decomposing the unit-cell tensor. We observe that this combining approach can significantly improve the computational cost even with maintaining the convergence accuracy of the free energy in the four-dimensional Ising model. In addition, we also show that a further improvement can be achieved in terms of the computational cost when our proposed approach is implemented in parallel on GPUs.

9 pages, 7 figures; Proceedings of the 41st International Symposium on Lattice Field Theory (Lattice 2024), July 28th - August 3rd, 2024, University of Liverpool, UK

References in corpus (10)

• Tensor-Entanglement-Filtering Renormalization Approach and Symmetry Protected Topological Order
• Tensor renormalization group approach to 2D classical lattice models
• Coarse-graining renormalization by higher-order singular value decomposition
• Anisotropic Tensor Renormalization Group
• Phase transition of four-dimensional Ising model with higher-order tensor renormalization group
• Tensor renormalization group approach to four-dimensional complex ${\varphi }^4$ theory at finite density
• Boundary Tensor Renormalization Group
• Critical endpoint of (3+1)-dimensional finite density $Z_3$ gauge-Higgs model with tensor renormalization group
• GPU-Acceleration of Tensor Renormalization with PyTorch using CUDA
• Randomized higher-order tensor renormalization group

Cited by in corpus (1)

• Triad representation for the anisotropic tensor renormalization group in four dimensions