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  Parallel time-dependent variational principle algorithm for matrix product states

Secular, P., Gourianov, N., Lubasch, M., Dolgov, S., Clark, S. R., & Jaksch, D. (2020). Parallel time-dependent variational principle algorithm for matrix product states. Physical Review B, 101(23): 235123. doi:10.1103/PhysRevB.101.235123.

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Item Permalink: https://hdl.handle.net/21.11116/0000-0006-9610-E Version Permalink: https://hdl.handle.net/21.11116/0000-000B-B4DA-4
Genre: Journal Article

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 Creators:
Secular, P.1, Author
Gourianov, N.2, Author
Lubasch, M.2, Author
Dolgov, S.3, Author
Clark, S. R.4, 5, Author           
Jaksch, D.2, 6, Author
Affiliations:
1Department of Physics, University of Bath, ou_persistent22              
2Clarendon Laboratory, Department of Physics, University of Oxford, ou_persistent22              
3Department of Mathematical Sciences, University of Bath, ou_persistent22              
4H.H. Wills Physics Laboratory, University of Bristol, ou_persistent22              
5Quantum Condensed Matter Dynamics, Condensed Matter Dynamics Department, Max Planck Institute for the Structure and Dynamics of Matter, Max Planck Society, ou_1938293              
6Centre for Quantum Technologies, National University of Singapore, ou_persistent22              

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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.

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Language(s): eng - English
 Dates: 2020-03-302020-01-102020-04-022020-06-052020-06-15
 Publication Status: Issued
 Pages: -
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 Table of Contents: -
 Rev. Type: Peer
 Identifiers: DOI: 10.1103/PhysRevB.101.235123
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Project name : P.S. thanks Jonathan Coulthard, James Grant, Fangli Liu, Frank Pollmann, and Leon Schoonderwoerd for helpful discussions. This research made use of the Balena High Performance Computing Service at the University of Bath, and used Tensor Network Theory Library code written by Sarah Al-Assam, Chris Goodyer, and Jonathan Coulthard. The density plots in this paper use the “Inferno” color map by Nathaniel J. Smith, and Stefan van der Walt. P.S. is supported by ClusterVision and the University of Bath. M.L. and D.J. are grateful for funding from the UK's Engineering and Physical Sciences Research Council (EPSRC) for Grants No. EP/M013243/1 and No. EP/K038311/1. D.J. also acknowledges EPSRC Grant No. EP/P01058X/1. S.R.C. gratefully acknowledges support from the EPSRC under Grant No. EP/P025110/2.
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Title: Physical Review B
  Abbreviation : Phys. Rev. B
Source Genre: Journal
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Publ. Info: Woodbury, NY : American Physical Society
Pages: - Volume / Issue: 101 (23) Sequence Number: 235123 Start / End Page: - Identifier: ISSN: 1098-0121
CoNE: https://pure.mpg.de/cone/journals/resource/954925225008