Anomalous symmetry protected topological states in interacting fermion systems

Understand

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.