2018/06/30 by Tomasz Maciążek, Adam Sawicki · 1 citation
Mathematics · Physics and Astronomy · #Abelian group #Algebraic structures and combinatorial models #Artificial intelligence #Complex system #Computer science #Mathematics #Physics #Pure mathematics #Quantum #Quantum many-body systems #Quantum mechanics #Random Matrices and Applications #Statistical physics #Statistics #math-ph #math.AT #math.MP #quant-ph
paper · pdf · doi:10.1007/s00220-019-03583-5
50 pages, v3: updated to reflect the published version. Commun. Math. Phys. (2019)
openalex publication_date 2019/10/09 · arxiv created 2019/10/10 · arxiv updated 2019/10/11 · openalex created_date 2020/11/23 · openalex updated_date 2026/08/05
Abstract We show that non-abelian quantum statistics can be studied using certain topological invariants which are the homology groups of configuration spaces. In particular, we formulate a general framework for describing quantum statistics of particles constrained to move in a topological space X . The framework involves a study of isomorphism classes of flat complex vector bundles over the configuration space of X which can be achieved by determining its homology groups. We apply this methodology for configuration spaces of graphs. As a conclusion, we provide families of graphs which are good candidates for studying simple effective models of anyon dynamics as well as models of non-abelian anyons on networks that are used in quantum computing. These conclusions are based on our solution of the so-called universal presentation problem for homology groups of graph configuration spaces for certain families of graphs.