A Strictly Single-Site DMRG Algorithm with Subspace Expansion

TL;DR

This paper presents a new single-site DMRG algorithm with subspace expansion that improves convergence speed and reduces computational cost, making tensor network simulations more efficient.

Contribution

The authors introduce a subspace expansion technique for single-site DMRG that avoids local minima and enhances speed, outperforming previous methods in efficiency and convergence.

Findings

Runtime improves by up to 2.5 times on Fermi-Hubbard model

Speed-up of approximately (d+1)/2 in applying H to |Ψ⟩

Compatible with parallelisation and non-abelian symmetries

Abstract

We introduce a strictly single-site DMRG algorithm based on the subspace expansion of the Alternating Minimal Energy (AMEn) method. The proposed new MPS basis enrichment method is sufficient to avoid local minima during the optimisation, similarly to the density matrix perturbation method, but computationally cheaper. Each application of $\hat H$ to $|\Psi\rangle$ in the central eigensolver is reduced in cost for a speed-up of $\approx (d + 1)/2$, with $d$ the physical site dimension. Further speed-ups result from cheaper auxiliary calculations and an often greatly improved convergence behaviour. Runtime to convergence improves by up to a factor of 2.5 on the Fermi-Hubbard model compared to the previous single-site method and by up to a factor of 3.9 compared to two-site DMRG. The method is compatible with real-space parallelisation and non-abelian symmetries.