The Zak phase defines a Z2 topological invariant for certain 1D AZC symmetry classes but vanishes under quaternionic anti-unitary symmetries, providing only partial information about topological phases in generalized Kitaev chains.
Index pairings in pres- ence of symmetries with applications to topological insulators.Commu- nications in Mathematical Physics, 343(2):477–513
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The Zak phase in topologically insulating chains: invariants and limitations
The Zak phase defines a Z2 topological invariant for certain 1D AZC symmetry classes but vanishes under quaternionic anti-unitary symmetries, providing only partial information about topological phases in generalized Kitaev chains.