We study spectral properties of Harper-like models by algebraic and combinatorial methods and derive sufficient conditions for the existence of spectral gaps with qualitative estimates. For this class the Chambers relation holds and we obtain an analytic expression for the representation dependent part. Models corresponding to the rectangular and triangular lattice are studied. In the second case we show that one class of spectral gaps is open for magnetic fields with “rational magnetic flux per unit cell.” A quantitative estimate for the gap widths is given for the anisotropic case and for “irrational magnetic flux” fulfilling some Liouville condition the spectrum is a Cantor set.
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