Strictly single-site DMRG algorithm with subspace expansion

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 optimization, similar to the density matrix perturbation method, but computationally cheaper. Each application of (H) over cap to broken vertical bar Psi > in the central eigensolver is reduced in cost for a speed-up of approximate to (d + 1)/2, with d the physical site dimension. Further speed-ups result from cheaper auxiliary calculations and an often greatly improved convergence behavior. 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 parallelization and non-Abelian symmetries.