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Integrability and quench dynamics in the spin-1 central spin XX model

by Long-Hin Tang, David M. Long, Anatoli Polkovnikov, Anushya Chandran, Pieter W. Claeys

This Submission thread is now published as

Submission summary

Authors (as registered SciPost users): Pieter W. Claeys · David Long
Submission information
Preprint Link:  (pdf)
Date accepted: 2023-05-22
Date submitted: 2023-05-09 13:01
Submitted by: Long, David
Submitted to: SciPost Physics
Ontological classification
Academic field: Physics
  • Atomic, Molecular and Optical Physics - Theory
  • Condensed Matter Physics - Theory
  • Quantum Physics
  • Statistical and Soft Matter Physics
Approaches: Theoretical, Computational


Central spin models provide an idealized description of interactions between a central degree of freedom and a mesoscopic environment of surrounding spins. We show that the family of models with a spin-1 at the center and XX interactions of arbitrary strength with surrounding spins is integrable. Specifically, we derive an extensive set of conserved quantities and obtain the exact eigenstates using the Bethe ansatz. As in the homogenous limit, the states divide into two exponentially large classes: bright states, in which the spin-1 is entangled with its surroundings, and dark states, in which it is not. On resonance, the bright states further break up into two classes depending on their weight on states with central spin polarization zero. These classes are probed in quench dynamics wherein they prevent the central spin from reaching thermal equilibrium. In the single spin-flip sector we explicitly construct the bright states and show that the central spin exhibits oscillatory dynamics as a consequence of the semilocalization of these eigenstates. We relate the integrability to the closely related class of integrable Richardson-Gaudin models, and conjecture that the spin-$s$ central spin XX model is integrable for any $s$.

Author comments upon resubmission

We would like to thank all three referees for their reports and very positive assessments of our manuscript. In the reworked manuscript we have taken into account all comments by the referees, including the optional suggestions by Dr. Dubail.

A more detailed response to specific questions and remarks can be found in our replies to the referee reports.

List of changes

Added a summary of the quench dynamics (sections 6 and 7) to the overview (section 2).
Included a new figure (Fig. 10) showing Poisson level spacing statistics in the spin-3/2 central spin XX model.
Various bibliographic changes, revisions of technical language, and corrections of typos.

Published as SciPost Phys. 15, 030 (2023)

Reports on this Submission

Anonymous Report 3 on 2023-5-11 (Invited Report)


The level statistics analysis is very convincing. I recommend that this revised version is accepted for publication.

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Anonymous Report 2 on 2023-5-10 (Invited Report)

  • Cite as: Anonymous, Report on arXiv:2212.04477v3, delivered 2023-05-10, doi: 10.21468/SciPost.Report.7178


Brand new construction of an integrable model.

Well written.

Detailed use of the integrability and the eigenstate structures to study the dynamics of the system and it lack of thermalisation.

A well argued and clear conjecture concerning a wider class of possible integrable models is provided.




The revisions have clarified and answered the requests that were made in the reports.

The level statistics plot is a very nice addition.

In my opinion it could have been publish in its initial form and, naturally, the revised version can, in my opinion be published as it is.

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

Report 1 by Jerome Dubail on 2023-5-9 (Invited Report)


The paper can be published as it is. I thank the authors for their answers to my comments.

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