A Class of Asymmetric Gapped Hamiltonians on Quantum Spin Chains and its Characterization III
- 98 Downloads
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.
Unable to display preview. Download preview PDF.
- BN12a.Bachmann, S., Nachtergaele, B.: Product vacua with boundary states and the classification of gapped phases. Commun. Math. Phys. 329(2), 509–544 (2014)Google Scholar
- M1.Matsui, T.: A characterization of pure finitely correlated states. Infinite Dimens. Anal. Quantum Probab. Relat. Topics 01, 647–661 (1998)Google Scholar
- NS.Nachtergaele, B., Sims, R.: Locality estimates for quantum spin systems. New Trends in Mathematical Physics. Selected contributions of the XVth International Congress on Mathematical Physics, Springer Verlag, pp. 591–614 (2009)Google Scholar
- O2.Ogata, Y.: A class of asymmetric gapped Hamiltonians on quantum spin chains and its classification II. Commun. Math. Phys. 348(3), 897–957 (2006)Google Scholar