Generalization of Benalcazar-Bernevig-Hughes model to arbitrary dimensions

The Benalcazar-Bernevig-Hughes (BBH) model [W. A. Benalcazar, B. A. Bernevig, and T. L. Hughes, Science 357, 61 (2017)], featuring a bulk quadrupole moment, edge dipole moments, and corner states, is a paradigm of both higher-order topological insulators and topological multipole insulators. In this work, we generalize the BBH model to arbitrary dimensions by utilizing the Clifford algebra. For the generalized BBH model, the analytical solution of corner states can be directly constructed in a unified way. Based on the solution of corner states and chiral symmetry analysis, we develop a general boundary projection method to extract the boundary Hamiltonians, which turns out to be the BBH models of lower dimension and reveals the dimensional hierarchy.

Automated summary

This paper generalizes the Benalcazar-Bernevig-Hughes (BBH) model to arbitrary dimensions and proposes a general boundary projection method for extracting the boundary Hamiltonians. By analyzing the analytical solution and chiral symmetry, the dimensional hierarchy of BBH models is revealed.