A class of asymmetric gapped Hamiltonians on quantum spin chains and its characterization III
Mathematical Physics
2017-03-08 v1 Statistical Mechanics
math.MP
Quantum Physics
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 -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.
Keywords
Cite
@article{arxiv.1606.05508,
title = {A class of asymmetric gapped Hamiltonians on quantum spin chains and its characterization III},
author = {Yoshiko Ogata},
journal= {arXiv preprint arXiv:1606.05508},
year = {2017}
}