An integrable deformed Landau-Lifshitz model with particle production?, by Marius de Leeuw, Andrea Fontanella, Juan Miguel Nieto García

SciPost Physics Home Authoring Refereeing Submit a manuscript About An integrable deformed Landau-Lifshitz model with particle production? Marius de Leeuw, Andrea Fontanella, Juan Miguel Nieto García SciPost Phys. 20, 041 (2026) · published 11 February 2026 doi: 10.21468/SciPostPhys.20.2.041 pdf BiBTeX RIS Submissions/Reports Abstract We discuss the continuum limit of a non-Hermitian deformation of the Heisenberg XXX spin chain. This model appeared in the classification of $4×4$ 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. × TY - JOURPB - SciPost FoundationDO - 10.21468/SciPostPhys.20.2.041TI - An integrable deformed Landau-Lifshitz model with particle production?PY - 2026/02/11UR - https://scipost.org/SciPostPhys.20.2.041JF - SciPost PhysicsJA - SciPost Phys.VL - 20IS - 2SP - 041A1 - de Leeuw, MariusAU - Fontanella, AndreaAU - Nieto García, Juan MiguelAB - We discuss the continuum limit of a non-Hermitian deformation of the Heisenberg XXX spin chain. This model appeared in the classification of $4×4$ 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.ER - × @Article{10.21468/SciPostPhys.20.2.041, title={{An integrable deformed Landau-Lifshitz model with particle production?}}, author={Marius de Leeuw and Andrea Fontanella and Juan Miguel Nieto García}, journal={SciPost Phys.}, volume={20}, pages={041}, year={2026}, publisher={SciPost}, doi={10.21468/SciPostPhys.20.2.041}, url={https://scipost.org/10.21468/SciPostPhys.20.2.041},} Ontology / Topics See full Ontology or Topics database. Integrability/integrable models Authors / Affiliations: mappings to Contributors and Organizations See all Organizations. 1 Marius de Leeuw, 1 Andrea Fontanella, 2 Juan Miguel Nieto García 1 Coláiste na Tríonóide Baile Átha Cliath / Trinity College Dublin [TCD] 2 Universität Hamburg / University of Hamburg [UH] Funders for the research work leading to this publication Deutsche Forschungsgemeinschaft / German Research FoundationDeutsche Forschungsgemeinschaft [DFG] European Research Council [ERC] Royal Society