Parallel time-dependent variational principle algorithm for matrix product states

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

Research output: Working paper


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 systems with long-range interactions. We benchmark the accuracy and performance of our implementation 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 chain with 1/r² interactions, which is challenging to compute sequentially. These results pave the way for the application of MPS to increasingly complex systems.
Original languageEnglish
Number of pages22
Publication statusSubmitted - 12 Dec 2019


  • computational
  • strongly-correlated
  • quantum
  • physics
  • chemistry
  • tensor networks
  • time evolution
  • simulation
  • long-range interactions
  • magnetism
  • TDVP
  • DMRG
  • MPS
  • MPI
  • OpenMP
  • parallelisation
  • spin chains
  • Ising model

ASJC Scopus subject areas

  • Software
  • Condensed Matter Physics
  • Atomic and Molecular Physics, and Optics
  • Computational Mathematics
  • Mathematical Physics
  • Modelling and Simulation

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