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The Benalcazar-Bernevig-Hughes (BBH) model [Science 357, 61 (2017)],featuring bulk quadrupole moment, edge dipole moments, and corner states, is aparadigm of both higher-order topological insulators and topological multipoleinsulators. In this work, we generalize the BBH model to arbitrary dimensionsby utilizing the Clifford algebra. For the generalized BBH model, theanalytical solution of corner states can be directly constructed in a unifiedway. Based on the solution of corner states and chiral symmetry analysis, wedevelop a general boundary projection method to extract the boundaryHamiltonians, which turns out to be the BBH models of lower dimension andreveals the dimensional hierarchy.

Generalization of Benalcazar-Bernevig-Hughes model to arbitrary dimensions