Majorana diagrammatics for quantum spin-1/2 models, by Thibault Noblet, Laura Messio, Riccardo Rossi

SciPost Physics Core Home Authoring Refereeing Submit a manuscript About Majorana diagrammatics for quantum spin-1/2 models Thibault Noblet, Laura Messio, Riccardo Rossi SciPost Phys. Core 9, 002 (2026) · published 16 January 2026 doi: 10.21468/SciPostPhysCore.9.1.002 pdf BiBTeX RIS Submissions/Reports Abstract A diagrammatic formalism for lattices of 1/2 is developed. It is based on an unconstrained mapping between spin and Majorana operators. This allows the use of standard tools of diagrammatic quantum many-body theory without requiring projections. We derive, in particular, the Feynman rules for the expansion around a color-preserving mean-field theory. We then present the numerical results obtained by computing the corrections up to second order for the Heisenberg model in one and two dimensions, showing that perturbative corrections are not only numerically important, but also qualitatively improve the results of mean-field theory. These results pave the way for the use of Majorana diagrammatic tools in theoretical and numerical studies of quantum spin systems. × TY - JOURPB - SciPost FoundationDO - 10.21468/SciPostPhysCore.9.1.002TI - Majorana diagrammatics for quantum spin-1/2 modelsPY - 2026/01/16UR - https://scipost.org/SciPostPhysCore.9.1.002JF - SciPost Physics CoreJA - SciPost Phys. CoreVL - 9IS - 1SP - 002A1 - Noblet, ThibaultAU - Messio, LauraAU - Rossi, RiccardoAB - A diagrammatic formalism for lattices of 1/2 is developed. It is based on an unconstrained mapping between spin and Majorana operators. This allows the use of standard tools of diagrammatic quantum many-body theory without requiring projections. We derive, in particular, the Feynman rules for the expansion around a color-preserving mean-field theory. We then present the numerical results obtained by computing the corrections up to second order for the Heisenberg model in one and two dimensions, showing that perturbative corrections are not only numerically important, but also qualitatively improve the results of mean-field theory. These results pave the way for the use of Majorana diagrammatic tools in theoretical and numerical studies of quantum spin systems.ER - × @Article{10.21468/SciPostPhysCore.9.1.002, title={{Majorana diagrammatics for quantum spin-1/2 models}}, author={Thibault Noblet and Laura Messio and Riccardo Rossi}, journal={SciPost Phys. Core}, volume={9}, pages={002}, year={2026}, publisher={SciPost}, doi={10.21468/SciPostPhysCore.9.1.002}, url={https://scipost.org/10.21468/SciPostPhysCore.9.1.002},} Ontology / Topics See full Ontology or Topics database. Antiferromagnets Authors / Affiliations: mappings to Contributors and Organizations See all Organizations. 1 2 3 Thibault Noblet, 1 2 3 Laura Messio, 1 2 3 4 Riccardo Rossi 1 Centre National de la Recherche Scientifique / French National Centre for Scientific Research [CNRS] 2 Sorbonne Université / Sorbonne University 3 Laboratoire de Physique Théorique de la Matière Condensée / Laboratory of Theoretical Physics of Condensed Matter [LPTMC] 4 École Polytechnique Fédérale de Lausanne [EPFL] Funder for the research work leading to this publication Staatssekretariat für Bildung, Forschung und Innovation