Non-Abelian hyperbolic band theory from supercells

• URL: http://arxiv.org/abs/2305.04945v2
• Date: Wed, 17 Jan 2024 16:09:00 GMT
• Title: Non-Abelian hyperbolic band theory from supercells
• Authors: Patrick M. Lenggenhager, Joseph Maciejko, Tom\'a\v{s} Bzdu\v{s}ek
• Abstract summary: hyperbolic lattices support non-Abelian Bloch states that have so far 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.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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 towards a complete band-theoretic characterization of hyperbolic lattices.

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