Hofstadter's Butterfly and Langlands Duality
Kazuki Ikeda
TL;DR
This paper explores the mathematical structure of the quantum Hall system through the lens of the Langlands program, revealing a duality that explains the fractal Hofstadter's butterfly pattern.
Contribution
It introduces the concept of quantum Langlands duality, connecting quantum groups and fractal structures in quantum Hall systems, offering a novel theoretical framework.
Findings
Identification of Langlands duality in quantum groups related to Hofstadter's butterfly
Mathematical connection between quantum Hall system and Langlands program
Proposal of a 'quantum Langlands duality' concept
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".
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.