发表机构
Yukawa Institute for Theoretical Physics, Kyoto University（京都大学汤川理论物理研究所）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文针对非可逆对称保护拓扑相，提出用对称置换的有限深度电路连接不同SPT相，构造矩阵乘积幺正算子并验证其对偶性预测。
AI 中文摘要
具有可逆对称性的1+1维对称保护拓扑（SPT）相可以通过对称纠缠器来表征：全局对称的有限深度局域幺正电路，从乘积态生成代表性基态。然而，对于非可逆对称性，不同的SPT相（例如三个$\mathrm{Rep}(D_8)$ SPT相）可能无法通过任何对称纠缠器连接。我们证明，这三个$\mathrm{Rep}(D_8)$ SPT相仍然可以通过对称置换的有限深度局域幺正电路连接，实现拓扑量子场论（TQFT）预测的对偶性。我们构造了一个显式的矩阵乘积幺正算子，连接三个$\mathrm{Rep}(D_8)$ SPT相中的两个，并展示其对弦序参数的作用再现了TQFT对偶性预测的任意子置换。
英文摘要
1+1D symmetry-protected topological (SPT) phases with invertible symmetry can be characterized by the symmetric entanglers: globally symmetric finite-depth local unitary circuits that generate representative ground states from a product state. For non-invertible symmetries, however, distinct SPT phases, such as the three $\mathrm{Rep}(D_8)$ SPT phases, may not be connected by any symmetric entangler. We show that the three $\mathrm{Rep}(D_8)$ SPT phases can nevertheless be connected by \emph{symmetry-permuting} finite-depth local unitary circuits, realizing dualities predicted by topological quantum field theory (TQFT). We construct an explicit matrix product unitary connecting two of the $\mathrm{Rep}(D_8)$ SPT phases, and show that its action on string order parameters reproduces the anyon permutation predicted by the TQFT duality.
Comments13 pages, 3 figures
