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

TL;DR

This paper demonstrates that probabilistic low-rank factorization significantly accelerates tensor network simulations of quantum many-body ground states, outperforming traditional methods especially near phase transitions.

Contribution

It introduces randomized low-rank factorization into tensor network algorithms, providing a faster alternative to deterministic SVD routines for ground state calculations.

Findings

Achieves up to 24x speedup in quasi-2D systems

Outperforms traditional SVD-based methods near phase transitions

Effective in TEBD and DMRG-style simulations

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.