Automorphic equivalence preserves the split property

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 ${\mathbb{Z}}_2$-index for gapped ground states of symmetry protected topological phases to show that the ${\mathbb{Z}}_2$-index is an invariant of gapped classification of phases containing fast-decaying interactions.

arXiv comment15 pages. Updated with minor revisions to match published version

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Cited by in corpus (7)

• A classification of phases of bosonic quantum lattice systems in one dimension
• The split and approximate split property in 2D systems: stability and absence of superselection sectors
• On ${\mathbb{Z}}_2$-indices for ground states of fermionic chains
• Relativistic Quantum Fields Are Universal Entanglement Embezzlers
• Quasi-Locality Bounds for Quantum Lattice Systems. Part II. Perturbations of Frustration-Free Spin Models with Gapped Ground States
• Stability of the spectral gap and ground state indistinguishability for a decorated AKLT model
• Automorphic equivalence within gapped phases in the bulk