Parallel time-dependent variational principle algorithm for matrix product states

Paul Secular*, Nikita Gourianov, Michael Lubasch, Sergey Dolgov, Stephen R. Clark, Dieter Jaksch

*Corresponding author for this work

Research output: Contribution to journalArticle (Academic Journal)peer-review

18 Citations (Scopus)
68 Downloads (Pure)


Combining the time-dependent variational principle (TDVP) algorithm with the parallelization scheme introduced by Stoudenmire and White for the density matrix renormalization group (DMRG), we present the first parallel matrix product state (MPS) algorithm capable of time evolving one-dimensional (1D) quantum lattice systems with long-range interactions. We benchmark the accuracy and performance of the algorithm by simulating quenches in the long-range Ising and XY models. We show that our code scales well up to 32 processes, with parallel efficiencies as high as 86%. Finally, we calculate the dynamical correlation function of a 201-site Heisenberg XXX spin chain with $1/r^2$ interactions, which is challenging to compute sequentially. These results pave the way for the application of tensor networks to increasingly complex many-body systems.
Original languageEnglish
Article number 235123
JournalPhysical Review B
Publication statusPublished - 5 Jun 2020


  • quant-ph
  • cond-mat.quant-gas
  • cond-mat.str-el
  • physics.comp-ph


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