Hofstadter's Butterfly and Langlands Duality
Mesoscale and Nanoscale Physics
2024-02-28 v1 High Energy Physics - Theory
Mathematical Physics
math.MP
Abstract
We dig out a deeper mathematical structure of the quantum Hall system from a perspective of the Langlands program. An algebraic expression of the Hamiltonian with the quantum group is a cornerstone. The Langlands duality of the quantum group sheds light on the fractal structure of Hofstadter's butterfly. This would imply a "quantum Langlands duality".
Cite
@article{arxiv.1708.00436,
title = {Hofstadter's Butterfly and Langlands Duality},
author = {Kazuki Ikeda},
journal= {arXiv preprint arXiv:1708.00436},
year = {2024}
}
Comments
9 pages, 1 figure