A Z(2)-Index of Symmetry Protected Topological Phases with Time Reversal Symmetry for Quantum Spin Chains

摘要

We introduce a Z(2)-index for time reversal invariant Hamiltonians with unique gapped ground state on quantum spin chains. We show this is an invariant of a C-1-classification of gapped Hamiltonians. Analogous results hold for more general on-site finite group symmetry, with the 2-cohomology class as the invariant.