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

Understand

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.