Many-body multipole index and bulk-boundary correspondence

Abstract

We propose new dipole and quadrupole indices for interacting insulators with point group symmetries. The proposed indices are defined in terms of many-body quantum multipole operators combined with the generator of the point group symmetry. Unlike the original multipole operators, these combined operators commute with Hamiltonian under the symmetry and therefore their eigenvalues are quantized. This enables a clear identification of nontrivial multipolar states. We calculate the multipole indices in representative models and show their effectiveness as order parameters. Furthermore, we demonstrate a bulk-boundary correspondence: a non-zero index implies the existence of edge/corner states under the the point group symmetry.

arXiv comment13 pages, 9 figures, to be published in Phys. Rev. B

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• Higher-order topological phases in crystalline and non-crystalline systems: a review
• Interaction and coherence in 2D bilayers
• Family of third-order topological insulators from Su-Schrieffer-Heeger stacking
• Quantized polarization in a generalized Rice-Mele model at arbitrary filling
• Projectification of point group symmetries with a background flux and Lieb-Schultz-Mattis theorem
• Polarization-based indices in quantum many-body systems: validity and extension beyond one dimension