Berlin 2024 – wissenschaftliches Programm
Bereiche | Tage | Auswahl | Suche | Aktualisierungen | Downloads | Hilfe
MP: Fachverband Theoretische und Mathematische Grundlagen der Physik
MP 10: AdS/CFT
MP 10.6: Vortrag
Donnerstag, 21. März 2024, 11:40–12:00, HL 001
HyperCells and HyperBloch: open-source software packages for studying hyperbolic lattices based on triangle groups — •Patrick M. Lenggenhager1,2,3,4,5, Joseph Maciejko4, and Tomáš Bzdušek1,2 — 1University of Zurich, Switzerland — 2Paul Scherrer Institute, Villigen PSI, Switzerland — 3ETH Zurich, Switzerland — 4University of Alberta, Edmonton, Canada — 5Max Planck Institute for the Physics of Complex Systems, Dresden, Germany
Hyperbolic lattices form the analogue of periodic structures in the hyperbolic plane and have been experimentally realized as networks in metamaterial platforms. The lattices possess discrete translation symmetry. However, due to the negative curvature, the resulting translation group is noncommutative which complicates not only the formulation of band theory but also the construction of periodic boundary conditions (PBC). Both infinite lattices and finite clusters with PBC can be conveniently described in terms of triangle groups.
I will introduce two recently released software packages, called HyperCells and HyperBloch, which provide convenient tools to construct connected and symmetric unit cells, including the associated translations, define arbitrary tight-binding models on them, and apply the supercell method for hyperbolic band theory to gain access at infinite-lattice eigenstates and -energies. The construction is based on an algebraic description of the lattice in terms of the corresponding triangle group, which facilitates a discussion of not only the translation symmetry but point-group symmetries as well. I will discuss examples and show some recent results.
Keywords: hyperbolic lattices; triangle groups; Bloch theorem; hyperbolic band theory