Quantum spin systems via probability and representation theory

Project funded by Swedish Research Council (Project grant), grant 2019-04185_VR. Participating organisations named by the source: University of Gothenburg. Funded amount: SEK 3,200,000, as stated by the source. Runs 2020-01-01 to 2023-12-31. Keywords: Naturvetenskap, Natural Sciences, Matematik, Mathematics, Sannolikhetsteori och statistik, Probability Theory and Statistics. Source: OpenAIRE Graph, from the funder's project data (collected by OpenAIRE on 2025-12-04); national funding data, not CORDIS. Abstract given by the source: The goal of this project is to further our understanding of mathematical properties of models from statistical physics, specifically quantum spin systems. Such models serve to explain phenomena such as phase-transitions in magnetic materials, based on simple assumptions about interactions at a sub-atomic level. A rigorous analysis of such models often has a rich mathematical content, linking several disciplines such as analysis, probability and algebra.Despite considerable effort over many years, properties of fundamental models such as the Heisenberg ferromagnet remain to be rigorously understood. In this project, we will make progress by developing novel methods based on connections to random permutations, random walks, and Schur-Weyl dualities in representation theory. By developing methods that combine probability- and representation theory, the project will lead to new results and insights about the Heisenberg and relevant related models, their phase-transitions and correlation structures.To complete the project, I will rely on my expertise in probabilistic methods for models from statistical physics, as well as pursue a deeper understanding of the connections with representation theory. An important part of the project will be to collaborate with experts in probability theory and mathematical physics within my network. Early in the project I will focus on models in simple geometries and develop tools that can later be applied to the main setting of regular lattices.

Original source.

Source: OpenAIRE Graph: projects of national funders, OpenAIRE, from the project data of Swedish Research Council. Retrieved 2026-10-28. Licence: Creative Commons Attribution 4.0 (OpenAIRE Graph). Selected metadata, adapted presentation; the publisher's record is authoritative. No endorsement by the source is implied. Licence: Creative Commons Attribution 4.0 (CC BY 4.0).

AI-assisted summary: The project "Quantum spin systems via probability and representation theory" is funded by the Swedish Research Council with a grant of SEK 3,200,000, running from January 1, 2020, to December 31, 2023, at the University of Gothenburg. Suggested technology pillar: simulation. Generated by AI from the public source text; it may contain errors and the original source is authoritative.