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

Abstract

We apply the charge pumping argument to fermionic tensor network representations of ddimensional 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 secondorder 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 obtained 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. arXiv:1912.08219v1 [cond-mat.str-el]