Towards a complete classification of fermionic symmetry protected topological phases in 3D and a general group supercohomology theory

Classification and construction of symmetry protected topological (SPT) phases in interacting boson and fermion systems have become a fascinating theoretical direction in recent years. It has been shown that the (generalized) group cohomology theory or cobordism theory can give rise to a complete classification of SPT phases in interacting boson/spin systems. Nevertheless, the construction and classification of SPT phases in interacting fermion systems are much more complicated, especially in 3D. In this work, we revisit this problem based on the equivalent class of fermionic symmetric local unitary (FSLU) transformations. We construct very general fixed point SPT wavefunctions for interacting fermion systems. We naturally reproduce the partial classifications given by special group super-cohomology theory, and we show that with an additional $\tilde{B}H^2(G_b, \mathbb Z_2)$ (the so-called obstruction free subgroup of $H^2(G_b, \mathbb Z_2)$) structure, a complete classification of SPT phases for three-dimensional interacting fermion systems with a total symmetry group $G_f=G_b\times \mathbb Z_2^f$ can be obtained for unitary symmetry group $G_b$. We also discuss the procedure of deriving a general group super-cohomology theory in arbitrary dimensions.Comment: 48 pages, 35 figures, published versio

Bulk induced phase transition in driven diffusive systems

This Letter studies a weakly and asymmetrically coupled three-lane driven diffusive system. A non-monotonically changing density profile in the middle lane has been observed. When the extreme value of the density profile reaches $\rho=0.5$, a bulk induced phase transition occurs which exhibits a shock and a continuously and smoothly decreasing density profile which crosses $\rho=0.5$ upstream or downstream of the shock. The existence of double shocks has also been observed. A mean-field approach has been used to interpret the numerical results obtained by Monte Carlo simulations. The current minimization principle has excluded the occurrence of two or more bulk induced shocks in the general case of nonzero lane changing rates

Historical Development of the Undergraduate Educational Model at BIT from the Perspective of Suzhi Education

From the perspective of suzhi education, this study analyses the historical development of the undergraduate educational model at Beijing Institute of Technology (BIT). It could be argued that BIT’s talent-cultivating system’s transformations from 1940 to 2020 echo Chinese higher education’s reform and development. This study concludes that BIT has experienced four phases: (1) from advocacy for general-specialized education’s integration to general education’s disappearance, (2) from the rectification of specialized education to the germination of suzhi and general education, (3) the flourishing of suzhi education and general education, and (4) the establishment of the Shuyuan System. The case of BIT reflects Chinese higher education’s development and the process of transforming from meritocracy to popularization. Chinese universities have changed their paradigm from emphasizing specialized education to highlighting suzhi education, as well as from focusing on training students into specialists to stressing students’ holistic development