Fermionic tensor networks for higher-order topological insulators from charge pumping
Abstract
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.
- Publication Date:
- Research Org.:
- Princeton Univ., NJ (United States)
- Sponsoring Org.:
- 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)
- OSTI Identifier:
- 1605502
- Alternate Identifier(s):
- OSTI ID: 1802869
- 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
- Resource Type:
- Published Article
- Journal Name:
- Physical Review B
- Additional Journal Information:
- Journal Name: Physical Review B Journal Volume: 101 Journal Issue: 11; Journal ID: ISSN 2469-9950
- Publisher:
- American Physical Society
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY; Materials Science; Physics
Citation Formats
Hackenbroich, Anna, Bernevig, B. Andrei, Schuch, Norbert, and Regnault, Nicolas. Fermionic tensor networks for higher-order topological insulators from charge pumping. United States: N. p., 2020.
Web. doi:10.1103/PhysRevB.101.115134.
Hackenbroich, Anna, Bernevig, B. Andrei, Schuch, Norbert, & Regnault, Nicolas. Fermionic tensor networks for higher-order topological insulators from charge pumping. United States. https://doi.org/10.1103/PhysRevB.101.115134
Hackenbroich, Anna, Bernevig, B. Andrei, Schuch, Norbert, and Regnault, Nicolas. Thu .
"Fermionic tensor networks for higher-order topological insulators from charge pumping". United States. https://doi.org/10.1103/PhysRevB.101.115134.
@article{osti_1605502,
title = {Fermionic tensor networks for higher-order topological insulators from charge pumping},
author = {Hackenbroich, Anna and Bernevig, B. Andrei and Schuch, Norbert and Regnault, Nicolas},
abstractNote = {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.},
doi = {10.1103/PhysRevB.101.115134},
journal = {Physical Review B},
number = 11,
volume = 101,
place = {United States},
year = {Thu Mar 19 00:00:00 EDT 2020},
month = {Thu Mar 19 00:00:00 EDT 2020}
}
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