Automorphic equivalence preserves the split property

Alvin Moon

doi:10.1016/j.jfa.2019.05.021

paper

Automorphic equivalence preserves the split property

arXiv:1903.00944 · doi:10.1016/j.jfa.2019.05.021

Abstract

We prove that the split property is a stable feature for spin chain states which are related by composition with *-automorphisms generated by power-law decaying interactions. We apply this to the theory of the $Z_{2}$ -index for gapped ground states of symmetry protected topological phases to show that the $Z_{2}$ -index is an invariant of gapped classification of phases containing fast-decaying interactions.

15 pages. Updated with minor revisions to match published version