The spectrum E = R²(e^p + e^{-p}) + (e^x + e^{-x}) from local P¹ × P¹ is identified with the almost Mathieu operator, yielding three spectral phases separated by transitions at R² = 1 and R² = e^β.
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Geometric Engineering and Almost Mathieu Operator
The spectrum E = R²(e^p + e^{-p}) + (e^x + e^{-x}) from local P¹ × P¹ is identified with the almost Mathieu operator, yielding three spectral phases separated by transitions at R² = 1 and R² = e^β.