English

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

R2 v1 2026-06-22T21:03:52.635Z