Accelerating two-dimensional tensor network contractions using QR decompositions

TL;DR

This paper introduces a QR-decomposition-based contraction scheme for tensor networks that significantly accelerates iPEPS computations, especially on GPUs, enabling faster and more accurate simulations of strongly correlated systems.

Contribution

The authors develop a QR-based contraction method for symmetric tensor networks that outperforms traditional approaches in speed, particularly on GPU hardware, without sacrificing accuracy.

Findings

Achieves up to 100x speedup over standard CTMRG methods.

Provides state-of-the-art results for Heisenberg and J1-J2 models.

Completes complex tensor network contractions in less than 1 hour on H100 GPU.

Abstract

Infinite projected entangled-pair states (iPEPS) provide a powerful tool for studying strongly correlated systems directly in the thermodynamic limit. A core component of the algorithm is the approximate contraction of the iPEPS, where the computational bottleneck typically lies in the singular value or eigenvalue decompositions involved in the renormalization step. This is particularly true on GPUs, where tensor contractions are substantially faster than these decompositions. Here we propose a contraction scheme for $C_{4v}$-symmetric tensor networks based on combining the corner transfer matrix renormalization group (CTMRG) with QR-decompositions which are substantially faster, especially on GPUs. Our approach achieves up to two orders of magnitude speedup compared to standard CTMRG without loss of accuracy and yields state-of-the-art results for the Heisenberg and $J_1$-$J_2$ models in less than 1 h on an H100 GPU.