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The equivalence of topological indices for $\mathrm{U}(1)\rtimes\mathbb{Z}_2$-symmetric quantum spin chains
Symmetry-protected topological (SPT) phases in quantum spin chains are distinguished by topological indices. Ogata's operator-algebraic indices apply to a broad range of symmetry classes without requiring continuous symmetry, whereas the elementary twist index of Tasaki requires $\mathrm{U}(1)$ symm
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