Year: 2024
Type: article
Abstract: Two-dimensional mirror symmetry enriched topological (SET) orders can be studied using the folding approach: it can be folded along the mirror axis and turned into a bilayer system on which the mirror symmetry acts as a ${\mathbb{Z}}_{2}$ layer-exchange symmetry. How mirror symmetry enriches the topological order is then encoded at the mirror axis, which is a gapped boundary of the folded bilayer system. Based on anyon-condensation theory, we classify possible ${\mathbb{Z}}_{2}$-symmetric gapped boundaries of the folded system. In particular, we derive an ${H}^{2}$ obstruction function, which corresponds to an ${H}^{3}$ obstruction for topological orders enriched by the time-reversal symmetry instead of mirror symmetry. We demonstrate that states with a nontrivial ${H}^{2}$ obstruction function can be constructed on the surface of a three-dimensional mirror SET order.
Authors: Zhaoyang Ding, Yang Qi
Institution: Fudan University
Language: English
Subfield: Atomic and Molecular Physics, and Optics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
Awards: G1967931889, 二维体系新拓扑物态和原型器件, G7006239907
OpenAlex ID: W4403706059