Anomalous symmetry protected topological states in interacting fermion systems (1810.12899v2)

Abstract: The classification and construction of symmetry protected topological (SPT) phases have been intensively studied in interacting systems recently. To our surprise, in interacting fermion systems, there exists a new class of the so-called anomalous SPT (ASPT) states which are only well defined on the boundary of a trivial fermionic bulk system. We first demonstrate the essential idea by considering an anomalous topological superconductor with time reversal symmetry $T^2=1$ in 2D. The physical reason is that the fermion parity might be changed locally by certain symmetry action, but is conserved if we introduce a bulk. Then we discuss the layer structure and systematical construction of ASPT states in interacting fermion systems in 2D with a total symmetry $G_f=G_b\times\mathbb{Z}_2^f$. Finally, potential experimental realizations of ASPT states are also addressed.