Tensor Renormalization Group with Randomized Singular Value Decomposition

TL;DR

This paper introduces a tensor renormalization group algorithm utilizing randomized SVD, reducing computational complexity and memory usage for 2D classical models, while maintaining accuracy at critical points.

Contribution

The authors develop a tensor renormalization group method based on randomized SVD, improving efficiency and scalability for 2D models compared to traditional approaches.

Findings

Reduced computational complexity to fifth power of bond dimension

Memory usage decreased to third power of bond dimension

Accurate results at critical points with oversampling parameter

Abstract

An algorithm of the tensor renormalization group is proposed based on a randomized algorithm for singular value decomposition. Our algorithm is applicable to a broad range of two-dimensional classical models. In the case of a square lattice, its computational complexity and memory usage are proportional to the fifth and the third power of the bond dimension, respectively, whereas those of the conventional implementation are of the sixth and the fourth power. The oversampling parameter larger than the bond dimension is sufficient to reproduce the same result as full singular value decomposition even at the critical point of the two-dimensional Ising model.