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

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.

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Item Permalink: https://hdl.handle.net/21.11116/0000-0008-7EC9-9 Version Permalink: https://hdl.handle.net/21.11116/0000-0009-4FD6-E
Genre: Journal Article

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PhysRevB.101.115134.pdf (Publisher version), 2MB
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https://doi.org/10.1103/PhysRevB.101.115134 (Publisher version)
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 Creators:
Hackenbroich, Anna1, Author
Bernevig, B. Andrei2, Author
Schuch, Norbert1, Author
Regnault, Nicolas1, Author
Affiliations:
1External Organizations, ou_persistent22              
2Max Planck Institute of Microstructure Physics, Max Planck Society, Weinberg 2, 06120 Halle, DE, ou_2415691              

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 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 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.

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Language(s): eng - English
 Dates: 2019-12-242020-02-192020-03-152020-03-19
 Publication Status: Issued
 Pages: -
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 Rev. Type: Peer
 Identifiers: DOI: 10.1103/PhysRevB.101.115134
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Project name : ERC Starting Grant WASCOSYS
Grant ID : 636201
Funding program : European Union’s Horizon 2020 research and innovation programme
Funding organization : European Research Council (ERC)
Project name : Germany’s Excellence Strategy
Grant ID : EXC-2111–390814868
Funding program : -
Funding organization : Deutsche Forschungsgemeinschaft (DFG)

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Title: Physical Review B
  Abbreviation : Phys. Rev. B
Source Genre: Journal
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Publ. Info: Woodbury, NY : American Physical Society
Pages: - Volume / Issue: 101 (11) Sequence Number: 115134 Start / End Page: - Identifier: ISSN: 1098-0121
CoNE: https://pure.mpg.de/cone/journals/resource/954925225008