Hofstadter butterfly as quantum phase diagram

DOI10.1063/1.1412464zbMath1019.81071arXivmath-ph/0101019OpenAlexW2161234691MaRDI QIDQ2774756

D. Osadchy, Joseph E. Avron

Publication date: 26 February 2002

Published in: Journal of Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math-ph/0101019

zbMATH Keywords

fractal structureHall conductanceGibbs phase rules

Mathematics Subject Classification ID

Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics (81Q05) Many-body theory; quantum Hall effect (81V70) Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs arising in equilibrium statistical mechanics (82B20) Fractals (28A80)

Related Items (18)

Beyond Diophantine Wannier diagrams: gap labelling for Bloch-Landau Hamiltonians ⋮ Asymptotic scaling and universality for skew products with factors in SL(2,) ⋮ Floquet engineering the Hofstadter butterfly in the square lattice and its effective Hamiltonian ⋮ Tight-binding reduction and topological equivalence in strong magnetic fields ⋮ Nests and chains of Hofstadter butterflies ⋮ Undecidability of the Spectral Gap ⋮ Positive Hausdorff dimensional spectrum for the critical almost Mathieu operator ⋮ Mapping the current-current correlation function near a quantum critical point ⋮ Discrete honeycombs, rational edges, and edge states ⋮ Properties of a class of quasi-periodic Schrödinger operators ⋮ Exponential Dynamical Localization: Criterion and Applications ⋮ APPLICATIONS OF MAGNETIC ΨDO TECHNIQUES TO SAPT ⋮ Topological origin and not purely antisymmetric wave functions of many-body states in the lowest Landau level ⋮ Golden mean renormalization for the almost Mathieu operator and related skew products ⋮ The Topological Bloch-Floquet Transform and Some Applications ⋮ The arithmetic version of the frequency transition conjecture: new proof and generalization ⋮ Equality of the bulk and edge Hall conductances in a mobility gap ⋮ Renormalization and universality of the Hofstadter spectrum

Cites Work

• Lipschitz continuity of gap boundaries for Hofstadter-like spectra
• Zero measure spectrum for the almost Mathieu operator
• Quantum group and magnetic translations Bethe ansatz for the Asbel-Hofstadter problem
• Fredholm indices and the phase diagram of quantum Hall systems
• A sum rule for the dispersion relations of the rational Harper equation
• The noncommutative geometry of the quantum Hall effect

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