Hofstadter's Butterfly and Langlands Duality

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".

arXiv comment9 pages, 1 figure

References in corpus (9)

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Cited by in corpus (12)

• Polaritonic Hofstadter Butterfly and Cavity-Control of the Quantized Hall Conductance
• Hyperbolic Band Theory under Magnetic Field and Dirac Cones on a Higher Genus Surface
• Topologically quantized current in quasiperiodic Thouless pumps
• Hyperbolic band theory through Higgs bundles
• Quantum Hall Effect and Langlands Program
• Fractal defect states in the Hofstadter butterfly
• Algebra of Hyperbolic Band Theory under Magnetic Field
• Fermionic fractional quantum Hall states: A modern approach to systems with bulk-edge correspondence
• Topological Aspects of Matters and Langlands Program
• Hofstadter-Toda spectral duality and quantum groups
• Universal Computation with Quantum Fields
• Gauge fields induced by curved spacetime