DMRG with Subspace Expansion on Symmetry-Protected Tensor Networks (C. Hubig)

  • Date: Mar 23, 2017
  • Time: 02:00 PM - 03:00 PM (Local Time Germany)
  • Speaker: Claudius Hubig
  • Department für Physik, Ludwig-Maximilians-Universität München
  • Room: Seminar room Theory Division - B 2.46
  • Host: MPQ, Theory Division
The Density Matrix Renormalisation Group when applied to matrix-product states is the method of choice for ground-state search on one-dimensional systems and still highly competitive even in unfavourable circumstances, such as critical systems and higher dimensions.

In this talk, I will discuss two separate methods which can be used to improve the computational efficiency of DMRG and related methods on matrix-product states and beyond. The first component is the implementation of both abelian and non-abelian symmetries in an entirely general way suitable also for higher-rank tensors as encountered in e.g.tree tensor network states. The second ingredient, the subspace expansion, allows for a fully single- site DMRG algorithm with favourable linear scaling in the local dimension of the tensor network. Even for common problems, this results in a considerable speed-up over the traditional two-site DMRG method or the density matrix perturbation approach for ground-state search at reduced algorithmic complexity. Additionally, the subspace expansion can potentially be used in a large set of other algorithms, such as the TDVP or the variational application of a matrix-product operator onto a matrix-product state.

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