English

Parallel time-dependent variational principle algorithm for matrix product states

Quantum Physics 2020-06-16 v3 Quantum Gases Strongly Correlated Electrons Computational Physics

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/r21/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.

Keywords

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

R2 v1 2026-06-23T12:44:26.434Z