A Strictly Single-Site DMRG Algorithm with Subspace Expansion

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 $|\Psi ⟩$ 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.

9 pages, 6 figures; added comparison with two-site DMRG

References in corpus (4)

• The density-matrix renormalization group in the age of matrix product states
• From density-matrix renormalization group to matrix product states
• Real-Space Parallel Density Matrix Renormalization Group
• Multigrid Algorithms for Tensor Network States

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