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

Journal Article · 19 March 2020 · Physical Review. B

DOI: https://doi.org/10.1103/physrevb.101.115134 · OSTI ID:1605502

Hackenbroich, Anna  ^[1]; Bernevig, B. Andrei ^[2]; Schuch, Norbert ^[1]; Regnault, Nicolas ^[3]

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1. Max-Planck-Institute of Quantum Optics, Garching (Germany); Munich Center for Quantum Science and Technology, München (Germany)
2. Princeton Univ., NJ (United States); Max-Planck-Institute of Microstructure Physics, Halle (Germany)
3. Princeton Univ., NJ (United States); Université PSL, Paris (France); Centre National de la Recherche Scientifique (CNRS), Paris (France); Sorbonne Univ., Paris (France); Université Paris-Diderot (France);

We apply the charge-pumping argument to fermionic tensor network representations of $$\textit{d}$$-dimensional topological insulators (TIs) to obtain tensor network states (TNSs) for ($$\textit{d}$$ + 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 $$\textit{d}$$ = 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 $$\textit{d}$$ = 2 for the obstructed atomic insulator (OAI) of the quadrupole model. The ($$\textit{d}$$ + 1)-dimensional TNSs obtained in this way have a constant bond dimension inherited from the $$\textit{d}$$-dimensional TNSs in all but one spatial direction, making them candidates for numerical applications. From the $$\textit{d}$$-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.

• Research Organization: Princeton Univ., NJ (United States)
• Sponsoring Organization: USDOE Office of Science (SC); European Research Council (ERC); European Union’s Horizon 2020; German Research Foundation (DFG); National Science Foundation (NSF); US Department of the Navy, Office of Naval Research (ONR); Packard Foundation; Schmidt Fund for Innovative Research; US Army Research Office (ARO); Agence Nationale de la Recherché (ANR)
• Grant/Contract Number: SC0016239; 636201; EXC-2111–390814868; ANR-17-CE30-0013-01; ANR-16- CE30-0025; DMR 1643312; 404513; N00014-14-1-0330; W911NF-12-1-0461
• OSTI ID: 1605502
• Alternate ID(s): OSTI ID: 1802869
• Journal Information: Physical Review. B, Vol. 101, Issue 11; ISSN 2469-9950
• Publisher: American Physical Society (APS)Copyright Statement
• Country of Publication: United States
• Language: English