发表机构
Yau Mathematical Sciences Center, Tsinghua University（清华大学丘成桐数学科学中心）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本研究证明阿贝尔Chern-Simons拓扑序的环面贝里矩阵可确定全体亏格扩展TQFT，归一化环面数据能重构有限二次模$(G,q)$，还验证了误差低于21.96%时最近行解码可恢复阿贝尔融合代数，结果适用于分数量子霍尔相等体系。
AI 中文摘要
我们证明，对于阿贝尔Chern-Simons拓扑序，环面贝里矩阵可确定全体亏格的扩展拓扑量子场论（TQFT）。我们将度量形变下投影贝里和乐的拓扑部分与阿贝尔Chern-Simons TQFT的映射类群表示相对应，并证明归一化的环面数据可重构其有限二次模$(G,q)$。近期研究表明$(G,q)$可在对称幺半自然同构意义下对扩展理论分类，因此无需选取$K$-矩阵表述，亏格一数据即可确定全体亏格理论。我们还证明，当归一化特征行误差$δ<21.96$%时，最近行解码可恢复阿贝尔融合代数，且与任意子数量无关。该结果适用于由偶格Chern-Simons理论描述的阿贝尔分数量子霍尔相和自旋液体相。
英文摘要
We show that for Abelian Chern-Simons topological orders, torus Berry matrices determine the all-genus extended TQFT. We identify the topological part of the projective Berry holonomy under metric deformations with the mapping-class-group representation of the Abelian Chern-Simons TQFT and prove that the normalized torus data reconstruct its finite quadratic module (G,q). Recent work showed that (G,q) classifies the extended theory up to symmetric monoidal natural isomorphism, and that the associated Abelian defect extension is determined by the pointed modular category C(G,q) arising from the same finite quadratic-module data. Therefore genus-one Berry data determine not only the all-genus bulk theory but also its associated defect structures without choosing a K-matrix presentation. We also prove that, for normalized character row errors $δ$<21.96%, nearest-row decoding recovers the Abelian fusion algebra independently of the number of anyons. The result applies to Abelian fractional quantum Hall and spin-liquid phases described by even-lattice Chern-Simons theories.
