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We discuss characterization of the polarization for insulators under the periodic boundary condition in terms of the Berry phase, clarifying confusing subtleties.
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Masaaki Nakamura and Johannes Voit, “Lattice twist operators and vertex operators in sine-gordon theory in one dimension,” Phys. Rev. B 65
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Karin M. Rabe, Charles H. Ahn, and Jean-Marc Triscone, Physics of Ferroelectrics (Springer-Verlag Berlin Heidelberg, 2007)
2007
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T. Hirano, H. Katsura, and Y. Hatsugai, “Topological classification of gapped spin chains: Quantized berry phase as a local order parameter,” Phys. Rev. B 77
Cited in the paper.
Lloyd N. Trefethen and J. A. C. Weideman, “The exponentially convergent trapezoidal rule,” SIAM Rev. 56
2014
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Y. Hatsugai and T. Fukui, “Bulk-edge correspondence in topological pumping,” Phys. Rev. B 94
2016
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Masaya Nakagawa and Shunsuke Furukawa, “Bosonic integer quantum hall effect as topological pumping,” Phys. Rev. B 95
2017
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Jun-Won Rhim, Jan Behrends, and Jens H. Bardarson, “Bulk-boundary correspondence from the intercellular zak phase,” Phys. Rev. B 95
2017
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Haruki Watanabe, “Insensitivity of bulk properties to the twisted boundary condition,” Phys. Rev. B 98
2018
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