An index for two-dimensional SPT states

Abstract

We define an index for 2d $G$-invariant invertible states of bosonic lattice systems in the thermodynamic limit for a finite symmetry group $G$. We show that this index is an invariant of SPT phase.

20 pages, 4 figures v3: Appendix A has been rewritten to make it more self-consistent. Lemma 2.6 from the previous version is replaced by Lemma A.6. Submitted to JMP

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• Stability of the spectral gap and ground state indistinguishability for a decorated AKLT model