Parallel time-dependent variational principle algorithm for matrix product states

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

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Abstract

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/r² 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 number235123
JournalPhysical Review B
Volume101
Issue number23
Early online date5 Jun 2020
DOIs
Publication statusPublished - 15 Jun 2020

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