On decomposable 1D fermion chains, the chiral many-body invariant equals the unpaired-end-fermion count, and the reflection invariant is fixed by charge and parity at the reflection center; adding translation symmetry yields a Z x Z2 x Z4 classification.
Topological insulators and superconductors
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Crystalline-equivalent topological phases of many-body fermionic systems in one dimension
On decomposable 1D fermion chains, the chiral many-body invariant equals the unpaired-end-fermion count, and the reflection invariant is fixed by charge and parity at the reflection center; adding translation symmetry yields a Z x Z2 x Z4 classification.