Probabilistic low-rank factorization accelerates tensor network simulations of critical quantum many-body ground states

Abstract: We provide evidence that randomized low-rank factorization is a powerful tool for the determination of the ground state properties of low-dimensional lattice Hamiltonians through tensor network techniques. In particular, we show that randomized matrix factorization outperforms truncated singular value decomposition based on state-of-the-art deterministic routines in TEBD and DMRG-style simulations, even when the system under study gets close to a phase transition: We report linear speedups in the bond- or local dimension, of up to 24 times in quasi-2D cylindrical systems.