Regensburg 2022 – wissenschaftliches Programm

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TT: Fachverband Tiefe Temperaturen

TT 16: Correlated Electrons: Method Development

TT 16.13: Vortrag

Mittwoch, 7. September 2022, 13:00–13:15, H10

Tetranacci polynomials in solid state phyics — •Nico Leumer — IPCMS, CNRS, Strasbourg

In mesoscopic physics, state of the art theoretical research relies not solely but to large extend on numerical investigations. Naturally, support from analytical side is important whenever possible, in particular to appeal physical intuition. For the first time, I will introduce to a broader audience so called Tetranacci polynomials, which offer a generic technique to analytic diagonalize a variety of model Hamiltonians for finite system size and when open/free boundary conditions are imposed. As perspective, this approach is applicable on discrete physical (sub-) systems owing at least two degrees of freedom per atom, such as the Kitaev chain or the 1d Rashba-nanowire in magnetic field positioned on superconducting substrate. The use extends further to the famous Su-Schrieffer-Heeger model or to topological trivial tight-binding chains having nearest and next nearest neighbor hopping. In my presentation, I elaborate that Tetranacci polynomials extend Bloch’s theorem and how they are related to eigenvectors and eigenvalues. Within the frame drawn by the illustrative example of the X-Y-chain in transverse magnetic field, I demonstrate how previous diagonalization approaches are recovered by the more general Tetranacci technique. The final part of my presentation is devoted to an overview of physically distinct systems hosting Tetranacci polynomials and their common spectral features overlooked in earlier studies.

[1] N. Leumer et al., J. Condens. Matter Phys. 32 445502 (2020)

[2] N. Leumer et al., Phys. Rev. B 103, 165432 (2021)