Fermionic tensor networks for higher-order topological insulators from charge pumping

Abstract

We apply the charge pumping argument to fermionic tensor network representations of d- dimensional topological insulators (TIs) to obtain tensor network states (TNSs) for (d + 1)- dimensional TIs. We exemplify the method by constructing a two-dimensional projected entangled pair state (PEPS) for a Chern insulator starting from a matrix product state (MPS) in d = 1 describing pumping in the Su-Schrieffer-Heeger (SSH) model. In extending the argument to second- order TIs, we build a three-dimensional TNS for a chiral hinge TI from a PEPS in d = 2 for the obstructed atomic insulator (OAI) of the quadrupole model. The (d + 1)-dimensional TNSs ob- tained in this way have a constant bond dimension inherited from the d-dimensional TNSs in all but one spatial direction, making them candidates for numerical applications. From the d-dimensional models, we identify gapped next-nearest neighbour Hamiltonians interpolating between the trivial and OAI phases of the fully dimerized SSH and quadrupole models, whose ground states are given by an MPS and a PEPS with a constant bond dimension equal to 2, respectively.