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Quantum quench dynamics in the transverse-field Ising model: A numerical expansion in linked rectangular clusters

by Jonas Richter, Tjark Heitmann, Robin Steinigeweg

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Submission summary

Authors (as registered SciPost users): Tjark Heitmann · Jonas Richter · Robin Steinigeweg
Submission information
Preprint Link:  (pdf)
Date accepted: 2020-08-28
Date submitted: 2020-07-24 14:26
Submitted by: Richter, Jonas
Submitted to: SciPost Physics
Ontological classification
Academic field: Physics
  • Condensed Matter Physics - Theory
  • Condensed Matter Physics - Computational
  • Quantum Physics
Approaches: Theoretical, Computational


We study quantum quenches in the transverse-field Ising model defined on different lattice geometries such as chains, two- and three-leg ladders, and two-dimensional square lattices. Starting from fully polarized initial states, we consider the dynamics of the transverse and the longitudinal magnetization for quenches to weak, strong, and critical values of the transverse field. To this end, we rely on an efficient combination of numerical linked cluster expansions (NLCEs) and a forward propagation of pure states in real time. As a main result, we demonstrate that NLCEs comprising solely rectangular clusters provide a promising approach to study the real-time dynamics of two-dimensional quantum many-body systems directly in the thermodynamic limit. By comparing to existing data from the literature, we unveil that NLCEs yield converged results on time scales which are competitive to other state-of-the-art numerical methods.

Author comments upon resubmission

Dear Editors,

we thank you very much for the careful handling of our manuscript

"Quantum quench dynamics in the transverse-field Ising model: A numerical
expansion in linked rectangular clusters",

which we hereby would like to resubmit.

In the revised version, we have incorporated various changes to the
text and the figures according to the requested changes by the three Referees.
We believe that these changes further improve the quality and the readability
of our manuscript. Additionally, in our replies to the reports, we have
addressed all questions and comments by the Referees.

Given the overall positive reports of the three Referees, as well as our
changes made to the text, we hope that our manuscript is now ready for
publication in SciPost Physics.

Yours sincerely,

Jonas Richter,
Tjark Heitmann,
Robin Steinigeweg.

List of changes

Summary of Changes

- various small changes throughout the text according to the comments by the
Referees (as described in our replies to the Referee reports)

- revision and extension of the explanations concerning the numerical method in
Sec. 3.1

- added new data for lower expansion orders in Fig. 2(b)

- added new data for transverse field g = 1 in Fig. 3(b)

- added new data for lower expansion order C = 10 in Fig. 5

- updated digitized ANN data for a larger system size in Fig. 7

- added a new section in the Appendix and the new Fig. 9, where additional
data for lower expansion orders and systems with open boundary conditions are

- updated all arXiv references with the published version where possible

Published as SciPost Phys. 9, 031 (2020)

Reports on this Submission

Anonymous Report 2 on 2020-8-26 (Invited Report)

  • Cite as: Anonymous, Report on arXiv:2005.03104v3, delivered 2020-08-26, doi: 10.21468/SciPost.Report.1943


The authors have clearly and satisfyingly addressed all my comments. With the changes and addition to their manuscript, it now reads very well and clearly demonstrates and discusses the advantages of the linked cluster expansion in quantum dynamics. The possible advantages and disadvantages of their method compared with other available methods is also clearly explained.

  • validity: top
  • significance: high
  • originality: high
  • clarity: top
  • formatting: excellent
  • grammar: excellent

Anonymous Report 1 on 2020-8-4 (Invited Report)

  • Cite as: Anonymous, Report on arXiv:2005.03104v3, delivered 2020-08-04, doi: 10.21468/SciPost.Report.1889


The authors have made several interesting changes to the manuscript and have answered my previous questions and suggestions. I especially find the new Fig. 5 very interesting and the discussion about the different types of cluster expansions will be very instructive. It is also good to know, that a Lanczos time evolution could be used as well. The revised version has improved and so I can fully recommend publication in SciPost Physics now.

Requested changes


  • validity: -
  • significance: -
  • originality: -
  • clarity: -
  • formatting: -
  • grammar: -

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