2019/04/02 by Yoshiko Ogata, Ogata, Yoshiko · 1 citation
Chemistry · Physics and Astronomy · #FOS: Physical sciences #Mathematical Physics (math-ph) #Molecular spectroscopy and chirality #Quantum Physics (quant-ph) #Quantum many-body systems #Statistical Mechanics (cond-mat.stat-mech) #Theoretical and Computational Physics
paper · pdf · doi:10.48550/arxiv.1904.01669
openalex publication_date 2019/04/02 · openalex created_date 2022/08/27 · openalex updated_date 2026/07/28
For the classification of SPT phases, defining an index is a central problem. In the famous paper [PTBO1], Pollmann, Tuner, Berg, and Oshikawa introduced \mathbb Z2-indices for injective matrix products states (MPS) which have either \mathbb Z2× \mathbb Z2 dihedral group (of π-rotations about x, y, and z-axes) symmetry, time-reversal symmetry, or reflection symmetry. The first two are on-site symmetries. In [O4], an index for on-site symmetries, which generalizes the index in [PTBO1], was introduced for general unique gapped ground state phases in quantum spin chains. It was proved that the index is an invariant of the C1-classification of SPT phases. The index for the reflection symmetry, which is not an on-site symmetry, was left as an open question. In this paper, we introduce a \mathbb Z2-index for the reflection symmetric unique gapped ground state phases, and complete the generalization problem of index by Pollmann et.al. We also show that the index is an invariant of the C1-classification.