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Interacting topological quantum chemistry of Mott atomic limits


Soldini, Martina O; Astrakhantsev, Nikita; Iraola, Mikel; Tiwari, Apoorv; Fischer, Mark H; Valentí, Roser; Vergniory, Maia G; Wagner, Glenn; Neupert, Titus (2023). Interacting topological quantum chemistry of Mott atomic limits. Physical Review B, 107:245145.

Abstract

Topological quantum chemistry (TQC) is a successful framework for identifying (noninteracting) topological materials. Based on the symmetry eigenvalues of Bloch eigenstates at maximal momenta, which are attainable from first principles calculations, a band structure can either be classified as an atomic limit, in other words adiabatically connected to independent electronic orbitals on the respective crystal lattice, or it is topological. For interacting systems, there is no single-particle band structure and hence, the TQC machinery grinds to a halt. We develop a framework analogous to TQC, but employing n-particle Green's function to classify interacting systems. Fundamentally, we define a class of interacting reference states that generalize the notion of atomic limits, which we call Mott atomic limits, and are symmetry protected topological states. Our formalism allows to fully classify these reference states (with n=2), which can themselves represent symmetry protected topological states. We present a comprehensive classification of such states in one dimension and provide numerical results on model systems. With this, we establish Mott atomic limit states as a generalization of the atomic limits to interacting systems.

Abstract

Topological quantum chemistry (TQC) is a successful framework for identifying (noninteracting) topological materials. Based on the symmetry eigenvalues of Bloch eigenstates at maximal momenta, which are attainable from first principles calculations, a band structure can either be classified as an atomic limit, in other words adiabatically connected to independent electronic orbitals on the respective crystal lattice, or it is topological. For interacting systems, there is no single-particle band structure and hence, the TQC machinery grinds to a halt. We develop a framework analogous to TQC, but employing n-particle Green's function to classify interacting systems. Fundamentally, we define a class of interacting reference states that generalize the notion of atomic limits, which we call Mott atomic limits, and are symmetry protected topological states. Our formalism allows to fully classify these reference states (with n=2), which can themselves represent symmetry protected topological states. We present a comprehensive classification of such states in one dimension and provide numerical results on model systems. With this, we establish Mott atomic limit states as a generalization of the atomic limits to interacting systems.

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Additional indexing

Item Type:Journal Article, refereed, original work
Communities & Collections:07 Faculty of Science > Physics Institute
Dewey Decimal Classification:530 Physics
Scopus Subject Areas:Physical Sciences > Electronic, Optical and Magnetic Materials
Physical Sciences > Condensed Matter Physics
Language:English
Date:29 June 2023
Deposited On:24 Nov 2023 10:31
Last Modified:29 Jun 2024 01:40
Publisher:American Physical Society
ISSN:2469-9950
OA Status:Green
Publisher DOI:https://doi.org/10.1103/PhysRevB.107.245145
  • Content: Published Version
  • Language: English