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 protected by general fermionic symmetry groups.

References in corpus (5)

• Matrix Product States, Projected Entangled Pair States, and variational renormalization group methods for quantum spin systems
• Fermionic SPT phases in higher dimensions and bosonization
• Entropy and Entanglement in Quantum Ground States
• Fermionic Matrix Product States and One-Dimensional Topological Phases
• Duality and Stacking of Bosonic and Fermionic SPT Phases

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