Bulletin of the American Physical Society
APS March Meeting 2018
Monday–Friday, March 5–9, 2018; Los Angeles, California
Session V44: Theory of Topological Protection and Related Issues in Correlated Electron Materials
2:30 PM–5:18 PM,
Thursday, March 8, 2018
LACC Room: 504
Sponsoring Unit: DCMP
Chair: Efstratios Manousakis, Florida State Univ
Abstract: V44.00002 : Fermionic Matrix Product States and One-Dimensional Short-Range Entangled Phases with Anti-Unitary Symmetries*
2:42 PM–2:54 PM
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 new 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 the cobordism classification to symmetry groups that are non-trivial extensions of fermion parity and time-reversal.
*U.S. Department of Energy, Office of Science, Office of High Energy Physics, Award Number DE-SC0011632.
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