SciPost Submission Page
An integrable deformed Landau-Lifshitz model with particle production?
by Marius de Leeuw, Andrea Fontanella, Juan Miguel Nieto García
Submission summary
| Authors (as registered SciPost users): | Juan Miguel Nieto García |
| Submission information | |
|---|---|
| Preprint Link: | scipost_202507_00048v1 (pdf) |
| Date submitted: | July 17, 2025, 5:35 p.m. |
| Submitted by: | Nieto García, Juan Miguel |
| Submitted to: | SciPost Physics |
| Ontological classification | |
|---|---|
| Academic field: | Physics |
| Specialties: |
|
| Approach: | Theoretical |
Abstract
We discuss the continuum limit of a non-Hermitian deformation of the Heisenberg XXX spin chain. This model appeared in the classification of $4\times4$ solutions of the Yang--Baxter equation and it has the particular feature that the transfer matrix is non-diagonalisable. We show that the model is given by a Drinfeld twist of the XXX spin chain and its continuum limit is a non-unitary deformation of the Landau–Lifshitz model. We compute the tower of conserved charges for this deformed Landau–Lifshitz model and show that they are generated by a boost operator. We furthermore show that it gives a non-vanishing $1\to 2$ S-matrix, where one of the outgoing particles has vanishing energy and momentum, and thus it does not fulfil the usual "no particle production" condition of integrability. We argue that this result is natural when looked from the point of view of the non-diagonalisability of the spin chain.
Author indications on fulfilling journal expectations
- Provide a novel and synergetic link between different research areas.
- Open a new pathway in an existing or a new research direction, with clear potential for multi-pronged follow-up work
- Detail a groundbreaking theoretical/experimental/computational discovery
- Present a breakthrough on a previously-identified and long-standing research stumbling block
Current status:
Reports on this Submission
Report
The authors have written a very interesting paper on an integrable, but non-unitary deformation of the XXX model. They then consider the continuum limit of this theory to find its classical analog. While not quite proving that the classical theory is integrable, they are able to construct an infinite tower of conserved quantities in involution, highly suggesting that the theory is integrable and a Lax pair can be constructed. Perhaps most interesting, they show that the theory can have 1 --> 2 particle production, where one of the two outgoing particles has zero momentum, which is a consequence of momentum conservation.
The paper is clearly written, and as I best as I can tell, free of any errors. I expect there to be a wide interest in the paper. For these reasons I recommend that it be published.
Recommendation
Publish (easily meets expectations and criteria for this Journal; among top 50%)