Accelerating two-dimensional tensor network contractions using QR-decompositions

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 and yields state-of-the-art results for the Heisenberg and $J_1$-$J_2$ models in about one hour on an H100 GPU.