An operator algebraic approach to symmetry defects and fractionalization

2024/10/30 by Kyle Kawagoe, Kawagoe, Kyle, Siddharth Vadnerkar +3 · 2 citations
Computer Science · Mathematics · #Approximation Theory and Sequence Spaces #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Matrix Theory and Algorithms #Operator Algebras (math.OA) #Strongly Correlated Electrons (cond-mat.str-el)

paper · pdf · doi:10.48550/arxiv.2410.23380

openalex publication_date 2024/10/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01

Abstract

We provide a superselection theory of symmetry defects in 2+1D symmetry enriched topological (SET) order in the infinite volume setting. For a finite symmetry group G with a unitary on-site action, our formalism produces a G-crossed braided tensor category GSec. This superselection theory is a direct generalization of the usual superselection theory of anyons, and thus is consistent with this standard analysis in the trivially graded component GSec₁. This framework also gives us a completely rigorous understanding of symmetry fractionalization. To demonstrate the utility of our formalism, we compute GSec explicitly in both short-range and long-range entangled spin systems with symmetry and recover the relevant skeletal data.

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