Non-Abelian hyperbolic band theory from supercells

Fuente: arXiv
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Autores principales: Lenggenhager, Patrick M., Maciejko, Joseph, Bzdušek, Tomáš
Formato: Preprint
Publicado: 2023
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author Lenggenhager, Patrick M.
Maciejko, Joseph
Bzdušek, Tomáš
author_facet Lenggenhager, Patrick M.
Maciejko, Joseph
Bzdušek, Tomáš
contents 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 towards a complete band-theoretic characterization of hyperbolic lattices.
format Preprint
id arxiv_https___arxiv_org_abs_2305_04945
institution arXiv
publishDate 2023
record_format arxiv
spellingShingle Non-Abelian hyperbolic band theory from supercells
Lenggenhager, Patrick M.
Maciejko, Joseph
Bzdušek, Tomáš
Mesoscale and Nanoscale Physics
Quantum Physics
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 towards a complete band-theoretic characterization of hyperbolic lattices.
title Non-Abelian hyperbolic band theory from supercells
topic Mesoscale and Nanoscale Physics
Quantum Physics
url https://arxiv.org/abs/2305.04945