2019/08/20 by Hideaki Oba, Oba, Hideaki · 1 citation
Computer Science · Mathematics · Physics and Astronomy · #Computational Physics (physics.comp-ph) #Computational Physics and Python Applications #FOS: Physical sciences #High Energy Physics - Lattice (hep-lat) #Quantum many-body systems #Statistical Mechanics (cond-mat.stat-mech) #Tensor decomposition and applications
paper · pdf · doi:10.48550/arxiv.1908.07295
openalex publication_date 2019/08/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The bottleneck part of anisotropic tensor renormalization group (ATRG) is a swapping bonds part which consists of a contraction of two tensors and a partial singular value decomposition of a matrix, and their computational costs are O(χ2d+1), where χ is the maximum bond dimension and d is the dimensionality of a system. We propose an alternative method for the swapping bonds part and it scales with O(χmax(d+3,7)), though the total cost of ATRG with the method remains O(χ2d+1). Moreover, the memory cost of the whole algorithm can be reduced from O(χ2d) to O(χmax(d+1,6)). We examine ATRG with or without the proposed method in the four-dimensional Ising model and find that the free energy density of the proposed algorithm is consistent with that of the original ATRG while the elapsed time is significantly reduced. We also compare the proposed algorithm with higher-order tensor renromalization group (HOTRG) and find that the value of the free energy density of the proposed algorithm is lower than that of HOTRG in the fixed elapsed time.