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 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-neighbor 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.

• Received 24 December 2019
• Revised 19 February 2020
• Accepted 19 February 2020

DOI:https://doi.org/10.1103/PhysRevB.101.115134

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Published by the American Physical Society