对称保护拓扑相、广义Laughlin变元和Orientifolds
Symmetry-protected Topological Phases, Generalized Laughlin Argument and Orientifolds
摘要：
我们推广Laughlin的通量插入参数，最初讨论的背景下的量子霍尔效应，拓扑相保护的非现场酉对称性，特别是奇偶对称性或奇偶对称性与现场酉对称性相结合。作为一个模型，我们讨论了具有CP对称性的二维空间中的费米子或玻色子系统，根据CPT定理，它们与时间反演对称的拓扑绝缘体（例如，量子自旋霍尔效应）。特别是，我们开发的稳定性/不稳定性（或“gappability”/“ingappability”）标准的非手征共形场论奇偶对称性，可能会出现作为一个边缘状态的一个保护拓扑相位。事实证明，一个必要的组成部分是考虑无定向表面上的边共形场论，例如克莱因瓶，它自然地产生于通过投影操作强制宇称对称。
英文摘要：
We generalize Laughlin's flux insertion argument, originally discussed in the context of the quantum Hall effect, to topological phases protected by non-on-site unitary symmetries, in particular by parity symmetry or parity symmetry combined with an on-site unitary symmetry. As a model, we discuss fermionic or bosonic systems in two spatial dimensions with CP symmetry, which are, by the CPT theorem, related to time-reversal symmetric topological insulators (e.g., the quantum spin Hall effect). In particular, we develop the stability/instability (or "gappability"/"ingappablity") criteria for non-chiral conformal field theories with parity symmetry that may emerge as an edge state of a symmetry-protected topological phase. A necessary ingredient, as it turns out, is to consider the edge conformal field theories on unoriented surfaces, such as the Klein bottle, which arises naturally from enforcing parity symmetry by a projection operation.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
