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arxiv: math-ph/0101019 · v2 · submitted 2001-01-16 · 🧮 math-ph · cond-mat.mes-hall· math.MP

Hofstadter butterfly as Quantum phase diagram

classification 🧮 math-ph cond-mat.mes-hallmath.MP
keywords phasediagrambutterflyhofstadterquantumcharacterizecoexistencecomponents
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The Hofstadter butterfly is viewed as a quantum phase diagram with infinitely many phases, labelled by their (integer) Hall conductance, and a fractal structure. We describe various properties of this phase diagram: We establish Gibbs phase rules; count the number of components of each phase, and characterize the set of multiple phase coexistence.

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