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Non-Abelian Hyperbolic Band Theory from Supercells


Lenggenhager, Patrick M; Maciejko, Joseph; Bzdušek, Tomáš (2023). Non-Abelian Hyperbolic Band Theory from Supercells. Physical Review Letters, 131(22):226401.

Abstract

Wave functions on periodic lattices are commonly described by Bloch band theory. Besides Abelian Bloch states labeled by a momentum vector, hyperbolic lattices support non-Abelian Bloch states that have so far eluded analytical treatments. By adapting the solid-state-physics notions of supercells and zone folding, we devise a method for the systematic construction of non-Abelian Bloch states. The method applies Abelian band theory to sequences of supercells, recursively built as symmetric aggregates of smaller cells, and enables a rapidly convergent computation of bulk spectra and eigenstates for both gapless and gapped tight-binding models. Our supercell method provides an efficient means of approximating the thermodynamic limit and marks a pivotal step toward a complete band-theoretic characterization of hyperbolic lattices.

Abstract

Wave functions on periodic lattices are commonly described by Bloch band theory. Besides Abelian Bloch states labeled by a momentum vector, hyperbolic lattices support non-Abelian Bloch states that have so far eluded analytical treatments. By adapting the solid-state-physics notions of supercells and zone folding, we devise a method for the systematic construction of non-Abelian Bloch states. The method applies Abelian band theory to sequences of supercells, recursively built as symmetric aggregates of smaller cells, and enables a rapidly convergent computation of bulk spectra and eigenstates for both gapless and gapped tight-binding models. Our supercell method provides an efficient means of approximating the thermodynamic limit and marks a pivotal step toward a complete band-theoretic characterization of hyperbolic lattices.

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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 > General Physics and Astronomy
Uncontrolled Keywords:General Physics and Astronomy
Language:English
Date:1 December 2023
Deposited On:06 Feb 2024 17:57
Last Modified:10 Jul 2024 03:17
Publisher:American Physical Society
ISSN:0031-9007
OA Status:Closed
Free access at:Publisher DOI. An embargo period may apply.
Publisher DOI:https://doi.org/10.1103/physrevlett.131.226401
PubMed ID:38101379
Project Information:
  • : FunderSNSF
  • : Grant ID185806
  • : Project TitleTopological band theory of driven and dissipative systems
  • : FunderSNSF
  • : Grant ID211310
  • : Project TitleNew paradigms for topological matter: delicate, multi-gap, hyperbolic
  • : FunderUniversity of Alberta
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  • : FunderCanada Research Chairs
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  • : FunderGovernment of Alberta
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  • : FunderPacific Institute for the Mathematical Sciences
  • : Grant ID
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  • : FunderNew Frontiers in Research Fund
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