Year: 2020
Type: article
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.
Institutions: Max Planck Institute of Quantum Optics, Munich Center for Quantum Science and Technology, Princeton University, Max Planck Institute of Microstructure Physics, Centre National de la Recherche Scientifique, Université Paris Sciences et Lettres, École Normale Supérieure - PSL, Sorbonne Université, Sorbonne Paris Cité, Laboratoire de Physique de l'Ecole Normale Supérieure, Université Paris Diderot
Language: English
Subfield: Atomic and Molecular Physics, and Optics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: hybrid
Funders: National Science Foundation, David and Lucile Packard Foundation, U.S. Department of Energy, Princeton Center for Complex Materials, European Commission, Deutsche Forschungsgemeinschaft, Agence Nationale de la Recherche, Multidisciplinary University Research Initiative, European Research Council, Office of Naval Research, Division of Materials Research, Army Research Office
Awards: Tensor-Network Methods for Strongly-Correlated Quantum Matter, G1338293535, G1349703009, G1375169175, Princeton Center for Complex Materials, G1768993395, G1889978188, G2586477669, G3224369381, Topological phases of matter : beyond two dimensions, G434337789, G4710139657, G5200267745, G6140129497, EAGER: Topological Semimetals, Insulators and Supersymmetry, G669191572, G6803667113, G6918153286, NEW TOPOLOGICAL FRONTIER, G732077798, G7452299184, G7601337859, EXC 2111: Munich Center for Quantum Science and Technology (MCQST), G8876996369
OpenAlex ID: W3010692230