High Performance Single-Site Finite DMRG on GPUs

The Density Matrix Renormalization Group (DMRG) algorithm is an essential tool in quantum physics. Nevertheless, the temporal and spatial expense of the DMRG algorithm grows dramatically with the dimension of systems and the number of sites. Meanwhile, data in the DMRG algorithm are tensors, and the DMRG algorithm has tensor computation-intensive characteristics. Considering that multi-core GPUs are suitable for matrix and tensor computation-intensive algorithms, this paper proposes a high-performance GPU implementation for the single-site finite DMRG algorithm, which includes three optimization strategies: efficient memory access, efficient tensor contraction, and data transfer using streaming. In the experiments with a varying number of sites, the optimized high-performance GPU implementation is 4.62 times faster on average and up to 13.23 times quicker than the Jax-GPU implementation in the TensorNetwork library.