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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
|Authors (as registered SciPost users):||Pieter W. Claeys · David Long|
|Preprint Link:||https://arxiv.org/abs/2212.04477v3 (pdf)|
|Date submitted:||2023-05-09 13:01|
|Submitted by:||Long, David|
|Submitted to:||SciPost Physics|
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 $s$.
Published as SciPost Phys. 15, 030 (2023)
Author comments upon resubmission
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.
Submission & Refereeing History
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Reports on this Submission
- 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.
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.