Statistics of Abelian topological excitations
Phys. Rev. B 113, 045143 – Published 26 January, 2026
DOI: https://doi.org/10.1103/g3nc-fwqg
Abstract
In this paper, we develop a novel theory that generalizes the concept of anyon statistics to Abelian topological excitations of any dimension. We axiomatize excitations as a selected collection of states and operators satisfying the configuration axiom and the locality axiom, purely based on many-body quantum mechanics. Upon these axioms, we define a rigorous and self-contained theory of statistics using only basic algebra that can be implemented on a computer. While our theory is developed independently, the results align with existing physical theories.
