Quantum spin liquid states with intrinsic topological orders supports fractionalized anyons excitations, which can carry fractional quantum numbers of spin rotational symmetry, time reversal symmetry and crystal symmetries. This symmetry fractionalization distinguishes different topologically ordered spin liquid states. Different ways of fractionalizing crystal symmetries can be classified through enumerating different combinations of fractional quantum numbers of each type of anyons, but some combinations are anomalous and can only be realized on the surface of a 3D topological crystalline insulator instead of a true 2D system. I will discuss the classification of (anomaly-free) symmetry fractionalization in gapped $\mathbb Z_2$ spin liquids.

戚杨于2005年毕业于清华大学物理系，2010年取得哈佛大学物理学博士学位，2010年7月至今在清华大学高等研究院担任副研究员，目前在加拿大Perimeter Institute for Theoretical Physics 作访问教授，主要研究方向是强关联系统中的理论问题，包括高温超导、量子自旋系统和冷原子体系中的强关联问题。研究中主要采用低能有效理论和场论等理论工具；并特别关注强关联体系中的量子临界现象和临界理论。此外，还对拓扑序和与量子相位相关的物理现象感兴趣。