Work

Triad representation for the anisotropic tensor renormalization group in four dimensions

Year: 2025

Type: article

Abstract: The development of tensor renormalization group (TRG) algorithm in higher dimensions is an important and urgent task, as the TRG is expected to provide a way to overcome the sign problem in lattice quantum chromodynamics (QCD) calculations at finite density. One possible approach that enables faster computations in four-dimensional lattice theories is the anisotropic tensor renormalization group (ATRG). However, the computational cost remains substantial and requires significant computational resources. In this paper, we propose a novel algorithm, called the triad-ATRG, which is based on the ATRG and other improved TRG variants with triad network representation. This method achieves lower scaling with respect to the bond dimension, while minimizing the loss of accuracy in the free energy and other physical quantities. We also present parallel implementations of both the ATRG and triad-ATRG on multiple GPUs, which significantly improve performance compared to CPU-based calculations for the four-dimensional system.

Source: Physical review. D/Physical review. D.

DOI: 10.1103/c3qc-tn48

Authors: Yuto Sugimoto, Shoichi Sasaki

Institution: Tohoku University

Language: English

Topic: Quantum many-body systems

Subfield: Atomic and Molecular Physics, and Optics

Field: Physics and Astronomy

Domain: Physical Sciences

Open Access status: hybrid

Funders: Tohoku University, Japan Society for the Promotion of Science

Award: テンソル繰り込み群の高次元ゲージ理論への応用