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arXiv · 1606.05508

A class of asymmetric gapped Hamiltonians on quantum spin chains and its characterization III

Yoshiko Ogata
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Abstract

In this paper, we consider 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 that1.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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Yoshiko Ogata. 2016-06-17. A class of asymmetric gapped Hamiltonians on quantum spin chains and its characterization III. https://doi.org/10.1007/s00220-016-2810-9

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