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Integrability and complexity in quantum spin chains

by Ben Craps, Marine De Clerck, Oleg Evnin, Philip Hacker

This Submission thread is now published as

Submission summary

Authors (as registered SciPost users): Marine De Clerck
Submission information
Preprint Link: scipost_202307_00036v2  (pdf)
Date accepted: 2024-01-09
Date submitted: 2023-12-06 12:07
Submitted by: De Clerck, Marine
Submitted to: SciPost Physics
Ontological classification
Academic field: Physics
  • Mathematical Physics
  • Quantum Physics


There is a widespread perception that dynamical evolution of integrable systems should be simpler in a quantifiable sense than the evolution of generic systems, though demonstrating this relation between integrability and reduced complexity in practice has remained elusive. We provide a connection of this sort by constructing a specific matrix in terms of the eigenvectors of a given quantum Hamiltonian. The null eigenvalues of this matrix are in one-to-one correspondence with conserved quantities that have simple locality properties (a hallmark of integrability). The typical magnitude of the eigenvalues, on the other hand, controls an explicit bound on Nielsen's complexity of the quantum evolution operator, defined in terms of the same locality specifications. We demonstrate how this connection works in a few concrete examples of quantum spin chains that possess diverse arrays of highly structured conservation laws mandated by integrability.

List of changes

We would like to thank both referees for their suggestions and constructive feedback. The manuscript has been updated with the following changes:

- Section 2.1, the introduction to section 3 and section 4.2 have been restructured as requested.

- We corrected the typos pointed out by the second referee, and changed the wording in a few places for clarity (including in the captions as requested).

- We added a reference to [16] in footnote 1, as well as a new paragraph containing [59-64] at the end of the conclusions section.

In relation to the request by the second referee to clearly contrast what is new compared to [6], we refer to the subsection "statement of results" in the introduction, which highlights the new results of the present work.

B. Craps, M. De Clerck, O. Evnin, P. Hacker

Published as SciPost Phys. 16, 041 (2024)

Reports on this Submission

Anonymous Report 2 on 2024-1-3 (Invited Report)


Same as in first report. With this new version, the readability has improved.


The authors have provided satisfactory replies to my comments, and the presentation has improved, especially in Section 2.1. I am happy to recommend this new version for publication in Scipost Physics.

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

Anonymous Report 1 on 2023-12-14 (Invited Report)


The authors carefully implemented the minor changes required by me and the other referee, so the manuscript is ready for publication in Scipost Physics.

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

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