Statistics of Abelian topological excitations

Hanyu Xue

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arXiv · 2412.07653

Statistics of Abelian topological excitations

Hanyu Xue

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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 and can be implemented on a computer. While our theory is developed independently, the results align with existing physical theories.

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Hanyu Xue. 2024-12-10. Statistics of Abelian topological excitations. https://arxiv.org/abs/2412.07653

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