Communications in Mathematical Physics

, Volume 352, Issue 3, pp 1205–1263 | Cite as

A Class of Asymmetric Gapped Hamiltonians on Quantum Spin Chains and its Characterization III

  • Yoshiko OgataEmail author


In this paper, we consider the classification problem of asymmetric gapped Hamiltonians, which are given as the non-degenerate part of the Hamiltonians introduced in [O1]. We consider the C 1-classification, which takes into account the effect of boundaries. We show that the left and right degeneracies of edge ground states are the complete invariant. As a corollary, we consider the bulk-classification problem. We study Hamiltonians that (1) are given by translation invariant finite range interactions, (2) are gapped in the bulk, (3) are frustration-free, (4) have uniformly bounded ground state degeneracy on finite intervals, and (5) have a unique bulk ground state. We show that for the bulk-classification, any such Hamiltonians are equivalent.


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© Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  1. 1.Graduate School of Mathematical SciencesThe University of TokyoTokyoJapan

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