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Journal Article

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


Bernevig,  B. Andrei
Max Planck Institute of Microstructure Physics, Max Planck Society;

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Hackenbroich, A., Bernevig, B. A., Schuch, N., & Regnault, N. (2020). Fermionic tensor networks for higher-order topological insulators from charge pumping. Physical Review B, 101(11): 115134. doi:10.1103/PhysRevB.101.115134.

Cite as: https://hdl.handle.net/21.11116/0000-0008-7EC9-9
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.