Title: Fermionic Matrix Product States and One-Dimensional Short-Range Entangled Phases with Anti-Unitary Symmetries,
Abstract: We extend the formalism of Matrix Product States (MPS) to describe
one-dimensional gapped systems of fermions with both unitary and anti-unitary
symmetries. Additionally, systems with orientation-reversing spatial symmetries
are considered. The short-ranged entangled phases of such systems are
classified by three invariants, which characterize the projective action of the
symmetry on edge states. We give interpretations of these invariants as
properties of states on the closed chain. The relationship between fermionic
MPS systems at an RG fixed point and equivariant algebras is exploited to
derive a group law for the stacking of fermionic phases. The result generalizes
known classifications to symmetry groups that are non-trivial extensions of
fermion parity and time-reversal.