Parallel time-dependent variational principle algorithm for matrix product states
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 interactions, which is challenging to compute sequentially. These results pave the way for the application of tensor networks to increasingly complex many-body systems.
Cite
@article{arxiv.1912.06127,
title = {Parallel time-dependent variational principle algorithm for matrix product states},
author = {Paul Secular and Nikita Gourianov and Michael Lubasch and Sergey Dolgov and Stephen R. Clark and Dieter Jaksch},
journal= {arXiv preprint arXiv:1912.06127},
year = {2020}
}
Comments
Version accepted for publication in Phys. Rev. B. Text clarified and references updated. Main text: 11 pages, 13 figures. Appendices: 3 pages, 3 figures. Supplemental material: 4 pages, 3 figures