English

$C^1$-classification of gapped parent Hamiltonians of quantum spin chains

Mathematical Physics 2015-06-22 v2 math.MP Quantum Physics

Abstract

We consider the C1C^1-classification of gapped Hamiltonians introduced in [Fannes-Nachtergaele-Werner, Nachtergaele] as parents Hamiltonians of translation invariant finitely correlated states. Within this family, we show that the number of edge modes, which is equal at the left and right edge, is the complete invariant. The construction proves that translation invariance of the `bulk' ground state does not need to be broken to establish C1C^1-equivalence, namely that the spin chain does not need to be blocked.

Keywords

Cite

@article{arxiv.1407.3924,
  title  = {$C^1$-classification of gapped parent Hamiltonians of quantum spin chains},
  author = {Sven Bachmann and Yoshiko Ogata},
  journal= {arXiv preprint arXiv:1407.3924},
  year   = {2015}
}

Comments

The asymmetric case considered in [v1] has been removed from [v2] because of an error in Lemma 4.1(b)