Anomaly-based classification of quantum phases in the presence of symmetries

1)应用于Lieb-Schultz-Mattis型可适性和多体chen数的广义边界条件[j]。2)在100t下观察到的自旋二聚体体系TlCuCl3的粒子-孔对称性破破[j] .中国物理学报，2001,26(7):7207。3)离散对称的扭曲边界条件和Lieb-Schultz-Mattis的不适用性[j]。4)准费米子化、玻色子化和临界准费米子理论[被JHEP接受]系统地分析了准费米子系统，系统地阐述了准费米子的临界理论。

1) Generalized boundary condition applied to Lieb-Schultz-Mattis type ingappabilities and many-body Chern numbers [Published on PRX 10, 031008] A generalized boundary condition is developed to study ingappability.2) Particle-hole symmetry breaking in a spin-dimer system TlCuCl3 observed at 100 T [Published on PRL 125, 267207]3) Twisted boundary condition and Lieb-Schultz-Mattis ingappability for discrete symmetries [Accepted by PRL] We generalize the ingappability theorem to discrete symmetries by a symmetry-twisting method.4) Parafermionization, bosonization, and critical parafermionic theories [Accepted by JHEP] Parafermionic systems are systematically analyzed and the parafermionic critical theories are systematically formulated.