Statistics of Abelian topological excitations

2024/12/10 by Xue, Hanyu · 3 citations
#FOS: Physical sciences #Mathematical Physics (math-ph) #Quantum Physics (quant-ph) #Strongly Correlated Electrons (cond-mat.str-el)

paper · doi:10.48550/arxiv.2412.07653

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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• Onsiteability of Higher-Form Symmetries
• Anyonic membranes and Pontryagin statistics
• Higher-Form Anomalies on Lattices

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